Mathematics

Quadratic-Equations

Easy

Question

In the Maths Olympiad of 2020 at Animal Planet, two representatives from the donkey’s side, while solving a quadratic equation, committed the following mistakes.
(i) One of them made a mistake in the constant term and got the roots as 5 and 9.
(ii) Another one committed an error in the coefficient of x and he got the roots as 12 and 4.
But in the meantime, they realised that they are wrong and they managed to get it right jointly. Find the quadratic equation.

x² + 4x + 14 = 0
2x² + 7x – 24 = 0
x² – 14x + 48 = 0
3x² – 17x + 52 = 0

The correct answer is: x² – 14x + 48 = 0

If one of roots of 2x² + ax + 32 = 0 is twice the other root, then the value of a is ________.

MathematicsQuadratic-Equations

Quadratic-Equations

Mathematics

If $square root of x minus 1 end root minus square root of x plus 1 end root plus 1 equals 0$ , then 4x is equal to

MathematicsQuadratic-Equations

Quadratic-Equations

Mathematics

In the equation $fraction numerator x left parenthesis x minus 1 right parenthesis minus left parenthesis m plus 1 right parenthesis over denominator left parenthesis x minus 1 right parenthesis left parenthesis m minus 1 right parenthesis end fraction equals x over m$ , the roots are equal when m = ____ .

MathematicsQuadratic-Equations

Quadratic-Equations

Mathematics

The roots of the equation x^2/3 + x^1/3 – 2 = 0 are ________.

MathematicsQuadratic-Equations

Quadratic-Equations

Mathematics

If the roots of the equation (a² + b²) x² – 2b(a + c)x + (b² + c²) = 0 are equal, then ________.

MathematicsQuadratic-Equations

Quadratic-Equations

Mathematics

Roots of the quadratic equation x² + x – (a + 1)(a + 2) = 0 are ________.

MathematicsQuadratic-Equations

Quadratic-Equations

Mathematics

For what value of a, the roots of the equation 2x² + 6x + a = 0, satisfy the condition $open parentheses alpha over beta close parentheses plus open parentheses beta over alpha close parentheses less than 2$ (where a and b are the roots of equation).

MathematicsQuadratic-Equations

Quadratic-Equations

Mathematics

One of the two students, while solving a quadratic equation in x, copied the constant term incorrectly and got the roots 3 and 2. The other copied the constant term and coefficient of x² correctly as –6 and 1 respectively. The correct roots are ____.

MathematicsQuadratic-Equations

Quadratic-Equations

Mathematics

If the roots of the equation (a – b)x² + (b – c)x + (c – a) = 0 are equal. Then

MathematicsQuadratic-Equations

Quadratic-Equations

Mathematics

If 2 is a root of the equation x² + bx + 12 = 0 and the equation x² + bx + q = 0 has equal roots, then q is equal to

MathematicsQuadratic-Equations

Quadratic-Equations

Mathematics

$square root of 30 plus square root of 30 plus square root of 30 plus square root of 30 plus.............. end root end root end root end root$ =

MathematicsQuadratic-Equations

Quadratic-Equations

Mathematics

The difference of the roots of 2y² – ky + 16 = 0 is $1 third$ . Find k.

MathematicsQuadratic-Equations

Quadratic-Equations

Mathematics

If (x + 2)(x + 4)(x + 6)(x + 8) = 945 and x is an integer, then find x.

MathematicsQuadratic-Equations

Quadratic-Equations

Mathematics

Rohan and Sohan were attempting to solve the quadratic equation, x² – ax + b = 0. Rohan copied the coefficient of x wrongly and obtained the roots as 4 and 12. Sohan copied the constant term wrongly and obtained the roots as -19 and 3. Find the correct roots.

MathematicsQuadratic-Equations

Quadratic-Equations

Mathematics

If the roots of the equation 3ax² + 2bx + c = 0 are in the ratio 2 : 3, then _____.

MathematicsQuadratic-Equations

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x2 + 4x + 14 = 02x2 + 7x – 24 = 0x2 – 14x + 48 = 03x2 – 17x + 52 = 0

The correct answer is: x2 – 14x + 48 = 0

Related Questions to study

If one of roots of 2x2 + ax + 32 = 0 is twice the other root, then the value of a is ________.

If one of roots of 2x2 + ax + 32 = 0 is twice the other root, then the value of a is ________.

If , then 4x is equal to

If , then 4x is equal to

In the equation , the roots are equal when m = ____ .

In the equation , the roots are equal when m = ____ .

The roots of the equation x2/3 + x1/3 – 2 = 0 are ________.

The roots of the equation x2/3 + x1/3 – 2 = 0 are ________.

If the roots of the equation (a2 + b2) x2 – 2b(a + c)x + (b2 + c2) = 0 are equal, then ________.

If the roots of the equation (a2 + b2) x2 – 2b(a + c)x + (b2 + c2) = 0 are equal, then ________.

Roots of the quadratic equation x2 + x – (a + 1)(a + 2) = 0 are ________.

Roots of the quadratic equation x2 + x – (a + 1)(a + 2) = 0 are ________.

For what value of a, the roots of the equation 2x2 + 6x + a = 0, satisfy the condition (where a and b are the roots of equation).

For what value of a, the roots of the equation 2x2 + 6x + a = 0, satisfy the condition (where a and b are the roots of equation).

One of the two students, while solving a quadratic equation in x, copied the constant term incorrectly and got the roots 3 and 2. The other copied the constant term and coefficient of x2 correctly as –6 and 1 respectively. The correct roots are ____.

One of the two students, while solving a quadratic equation in x, copied the constant term incorrectly and got the roots 3 and 2. The other copied the constant term and coefficient of x2 correctly as –6 and 1 respectively. The correct roots are ____.

If the roots of the equation (a – b)x2 + (b – c)x + (c – a) = 0 are equal. Then

If the roots of the equation (a – b)x2 + (b – c)x + (c – a) = 0 are equal. Then

If 2 is a root of the equation x2 + bx + 12 = 0 and the equation x2 + bx + q = 0 has equal roots, then q is equal to

If 2 is a root of the equation x2 + bx + 12 = 0 and the equation x2 + bx + q = 0 has equal roots, then q is equal to

=

=

The difference of the roots of 2y2 – ky + 16 = 0 is . Find k.

The difference of the roots of 2y2 – ky + 16 = 0 is . Find k.

If (x + 2)(x + 4)(x + 6)(x + 8) = 945 and x is an integer, then find x.

If (x + 2)(x + 4)(x + 6)(x + 8) = 945 and x is an integer, then find x.

Rohan and Sohan were attempting to solve the quadratic equation, x2 – ax + b = 0. Rohan copied the coefficient of x wrongly and obtained the roots as 4 and 12. Sohan copied the constant term wrongly and obtained the roots as -19 and 3. Find the correct roots.

Rohan and Sohan were attempting to solve the quadratic equation, x2 – ax + b = 0. Rohan copied the coefficient of x wrongly and obtained the roots as 4 and 12. Sohan copied the constant term wrongly and obtained the roots as -19 and 3. Find the correct roots.

If the roots of the equation 3ax2 + 2bx + c = 0 are in the ratio 2 : 3, then _____.

If the roots of the equation 3ax2 + 2bx + c = 0 are in the ratio 2 : 3, then _____.

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x² + 4x + 14 = 0
2x² + 7x – 24 = 0
x² – 14x + 48 = 0
3x² – 17x + 52 = 0

The correct answer is: x² – 14x + 48 = 0

If one of roots of 2x² + ax + 32 = 0 is twice the other root, then the value of a is ________.

If one of roots of 2x² + ax + 32 = 0 is twice the other root, then the value of a is ________.

If $square root of x minus 1 end root minus square root of x plus 1 end root plus 1 equals 0$ , then 4x is equal to

If $square root of x minus 1 end root minus square root of x plus 1 end root plus 1 equals 0$ , then 4x is equal to

The roots of the equation x^2/3 + x^1/3 – 2 = 0 are ________.

The roots of the equation x^2/3 + x^1/3 – 2 = 0 are ________.

If the roots of the equation (a² + b²) x² – 2b(a + c)x + (b² + c²) = 0 are equal, then ________.

If the roots of the equation (a² + b²) x² – 2b(a + c)x + (b² + c²) = 0 are equal, then ________.

Roots of the quadratic equation x² + x – (a + 1)(a + 2) = 0 are ________.

Roots of the quadratic equation x² + x – (a + 1)(a + 2) = 0 are ________.

For what value of a, the roots of the equation 2x² + 6x + a = 0, satisfy the condition $open parentheses alpha over beta close parentheses plus open parentheses beta over alpha close parentheses less than 2$ (where a and b are the roots of equation).

For what value of a, the roots of the equation 2x² + 6x + a = 0, satisfy the condition $open parentheses alpha over beta close parentheses plus open parentheses beta over alpha close parentheses less than 2$ (where a and b are the roots of equation).

One of the two students, while solving a quadratic equation in x, copied the constant term incorrectly and got the roots 3 and 2. The other copied the constant term and coefficient of x² correctly as –6 and 1 respectively. The correct roots are ____.

One of the two students, while solving a quadratic equation in x, copied the constant term incorrectly and got the roots 3 and 2. The other copied the constant term and coefficient of x² correctly as –6 and 1 respectively. The correct roots are ____.

If the roots of the equation (a – b)x² + (b – c)x + (c – a) = 0 are equal. Then

If the roots of the equation (a – b)x² + (b – c)x + (c – a) = 0 are equal. Then

If 2 is a root of the equation x² + bx + 12 = 0 and the equation x² + bx + q = 0 has equal roots, then q is equal to

If 2 is a root of the equation x² + bx + 12 = 0 and the equation x² + bx + q = 0 has equal roots, then q is equal to

$square root of 30 plus square root of 30 plus square root of 30 plus square root of 30 plus.............. end root end root end root end root$ =

$square root of 30 plus square root of 30 plus square root of 30 plus square root of 30 plus.............. end root end root end root end root$ =

The difference of the roots of 2y² – ky + 16 = 0 is $1 third$ . Find k.

The difference of the roots of 2y² – ky + 16 = 0 is $1 third$ . Find k.

Rohan and Sohan were attempting to solve the quadratic equation, x² – ax + b = 0. Rohan copied the coefficient of x wrongly and obtained the roots as 4 and 12. Sohan copied the constant term wrongly and obtained the roots as -19 and 3. Find the correct roots.

Rohan and Sohan were attempting to solve the quadratic equation, x² – ax + b = 0. Rohan copied the coefficient of x wrongly and obtained the roots as 4 and 12. Sohan copied the constant term wrongly and obtained the roots as -19 and 3. Find the correct roots.

If the roots of the equation 3ax² + 2bx + c = 0 are in the ratio 2 : 3, then _____.

If the roots of the equation 3ax² + 2bx + c = 0 are in the ratio 2 : 3, then _____.