Mathematics

Quadratic-Equations

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Question

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

2b = a + c
2a = b + c
2c = a + b
$\frac{1}{b} = \frac{1}{a} + \frac{1}{c}$

The correct answer is: 2a = b + c

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

Quadratic-Equations

Mathematics

If the roots of the quadratic equation ax² + bx + c = 0 are α and β, then the equation whose roots are α² and β² is _____.

MathematicsQuadratic-Equations

Quadratic-Equations

Mathematics

What are the values of x which satisfy the equation, $square root of 5 x minus 6 end root plus fraction numerator 1 over denominator square root of 5 x minus 6 end root end fraction equals 10 over 3 ?$

MathematicsQuadratic-Equations

Quadratic-Equations

Mathematics

Which of the following are the roots of the equation |x|² + |x| - 6 = 0?
A) 2 B) -2 C) 3 D) -3

MathematicsQuadratic-Equations

Quadratic-Equations

Mathematics

If the quadratic equation (a² - b²)x² + (b² - c²)x + (c² - a²) = 0 has equal roots, then which of the following is true?

MathematicsQuadratic-Equations

Quadratic-Equations

Mathematics

Find the range of the values of x which satisfy the inequation, x² – 7x + 3 < 2x + 25.

MathematicsQuadratic-Equations

Quadratic-Equations

Mathematics

If the sum of the squares of three consecutive odd natural numbers is 155, then their product will be equal to _____.

MathematicsQuadratic-Equations

Quadratic-Equations

Mathematics

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

2b = a + c2a = b + c2c = a + b

The correct answer is: 2a = b + c

Related Questions to study

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 _____.

If the roots of the quadratic equation ax2 + bx + c = 0 are α and β, then the equation whose roots are α2 and β2 is _____.

If the roots of the quadratic equation ax2 + bx + c = 0 are α and β, then the equation whose roots are α2 and β2 is _____.

What are the values of x which satisfy the equation,

What are the values of x which satisfy the equation,

Which of the following are the roots of the equation |x|2 + |x| - 6 = 0?A) 2 B) -2 C) 3 D) -3

Which of the following are the roots of the equation |x|2 + |x| - 6 = 0?A) 2 B) -2 C) 3 D) -3

If the quadratic equation (a2 - b2)x2 + (b2 - c2)x + (c2 - a2) = 0 has equal roots, then which of the following is true?

If the quadratic equation (a2 - b2)x2 + (b2 - c2)x + (c2 - a2) = 0 has equal roots, then which of the following is true?

Find the range of the values of x which satisfy the inequation, x2 – 7x + 3 < 2x + 25.

Find the range of the values of x which satisfy the inequation, x2 – 7x + 3 < 2x + 25.

If the sum of the squares of three consecutive odd natural numbers is 155, then their product will be equal to _____.

If the sum of the squares of three consecutive odd natural numbers is 155, then their product will be equal to _____.

The solution of the inequation, 15x2 – 31x + 14 < 0 is given by _____.

The solution of the inequation, 15x2 – 31x + 14 < 0 is given by _____.

If (x + 1) (x + 3) (x + 5) (x + 7) = 5760, find the real values of x.

If (x + 1) (x + 3) (x + 5) (x + 7) = 5760, find the real values of x.

If 3 · 22x+1 – 5 · 2x+2 + 16 = 0 and x is an integer, find the value of x.

If 3 · 22x+1 – 5 · 2x+2 + 16 = 0 and x is an integer, find the value of x.

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

2b = a + c
2a = b + c
2c = a + b
$\frac{1}{b} = \frac{1}{a} + \frac{1}{c}$

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 _____.

If the roots of the quadratic equation ax² + bx + c = 0 are α and β, then the equation whose roots are α² and β² is _____.

If the roots of the quadratic equation ax² + bx + c = 0 are α and β, then the equation whose roots are α² and β² is _____.

What are the values of x which satisfy the equation, $square root of 5 x minus 6 end root plus fraction numerator 1 over denominator square root of 5 x minus 6 end root end fraction equals 10 over 3 ?$

What are the values of x which satisfy the equation, $square root of 5 x minus 6 end root plus fraction numerator 1 over denominator square root of 5 x minus 6 end root end fraction equals 10 over 3 ?$

Which of the following are the roots of the equation |x|² + |x| - 6 = 0?
A) 2 B) -2 C) 3 D) -3

Which of the following are the roots of the equation |x|² + |x| - 6 = 0?
A) 2 B) -2 C) 3 D) -3

If the quadratic equation (a² - b²)x² + (b² - c²)x + (c² - a²) = 0 has equal roots, then which of the following is true?

If the quadratic equation (a² - b²)x² + (b² - c²)x + (c² - a²) = 0 has equal roots, then which of the following is true?

Find the range of the values of x which satisfy the inequation, x² – 7x + 3 < 2x + 25.

Find the range of the values of x which satisfy the inequation, x² – 7x + 3 < 2x + 25.

The solution of the inequation, 15x² – 31x + 14 < 0 is given by _____.

The solution of the inequation, 15x² – 31x + 14 < 0 is given by _____.

If 3 · 2^2x+1 – 5 · 2^x+2 + 16 = 0 and x is an integer, find the value of x.

If 3 · 2^2x+1 – 5 · 2^x+2 + 16 = 0 and x is an integer, find the value of x.