Mathematics

Quadratic-Equations

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Question

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

b² + c² = a²
b² + c² = 2a²
b² - c² = 2a²
a²= b² + 2c²

The correct answer is: b² + c² = 2a²

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

If α and β are the roots of the equation x² – 6x + 8 = 0, then find the value of α² + β²

MathematicsQuadratic-Equations

Quadratic-Equations

Mathematics

Form a quadratic equation with rational coefficients, one of whose roots is $3 plus square root of 5$ .

MathematicsQuadratic-Equations

Quadratic-Equations

Mathematics

If the sum of the roots of the equation kx² – 3x + 9 = 0 is $3 over 11$ , then find the product of the roots of that equation.

MathematicsQuadratic-Equations

Quadratic-Equations

Mathematics

Discuss the nature of the roots of the equation 4x² – 2x + 1 = 0.

MathematicsQuadratic-Equations

Quadratic-Equations

Mathematics

Find the roots of the equation 4x² – 13x + 10 = 0

MathematicsQuadratic-Equations

10th-Grade-Mathematics-Australia

Weekly-Tests-

Find the values of k for each of the following quadratic equations, so that they have two equal roots. kx (x – 2) + 6 = 0 ?

Weekly-Tests-10th-Grade-Mathematics-Australia

10th-Grade-Mathematics-Australia

Weekly-Tests-

Find the values of k for each of the following quadratic equations, so that they have two equal roots. 2x² + kx + 3 = 0

Weekly-Tests-10th-Grade-Mathematics-Australia

10th-Grade-Mathematics-Australia

Weekly-Tests-

Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.

Weekly-Tests-10th-Grade-Mathematics-Australia

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

b2 + c2 = a2b2 + c2 = 2a2b2 - c2 = 2a2 a2= b2 + 2c2

The correct answer is: b2 + c2 = 2a2

Related Questions to study

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.

Solve for x, |x|2 – 7|x| + 12 = 0.

Solve for x, |x|2 – 7|x| + 12 = 0.

Solve for x: 3x+1 + 32x+1 = 270

Solve for x: 3x+1 + 32x+1 = 270

If α and β are the roots of the equation x2 – 6x + 8 = 0, then find the value of α2 + β2

If α and β are the roots of the equation x2 – 6x + 8 = 0, then find the value of α2 + β2

Form a quadratic equation with rational coefficients, one of whose roots is .

Form a quadratic equation with rational coefficients, one of whose roots is .

If the sum of the roots of the equation kx2 – 3x + 9 = 0 is , then find the product of the roots of that equation.

If the sum of the roots of the equation kx2 – 3x + 9 = 0 is , then find the product of the roots of that equation.

Discuss the nature of the roots of the equation 4x2 – 2x + 1 = 0.

Discuss the nature of the roots of the equation 4x2 – 2x + 1 = 0.

Find the roots of the equation 4x2 – 13x + 10 = 0

Find the roots of the equation 4x2 – 13x + 10 = 0

Find the values of k for each of the following quadratic equations, so that they have two equal roots. kx (x – 2) + 6 = 0 ?

Find the values of k for each of the following quadratic equations, so that they have two equal roots. kx (x – 2) + 6 = 0 ?

Find the values of k for each of the following quadratic equations, so that they have two equal roots. 2x2 + kx + 3 = 0

Find the values of k for each of the following quadratic equations, so that they have two equal roots. 2x2 + kx + 3 = 0

Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.

Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.

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

b² + c² = a²
b² + c² = 2a²
b² - c² = 2a²
a²= b² + 2c²

The correct answer is: b² + c² = 2a²

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.

Solve for x, |x|² – 7|x| + 12 = 0.

Solve for x, |x|² – 7|x| + 12 = 0.

Solve for x: 3^x+1 + 3^2x+1 = 270

Solve for x: 3^x+1 + 3^2x+1 = 270

If α and β are the roots of the equation x² – 6x + 8 = 0, then find the value of α² + β²

If α and β are the roots of the equation x² – 6x + 8 = 0, then find the value of α² + β²

Form a quadratic equation with rational coefficients, one of whose roots is $3 plus square root of 5$ .

Form a quadratic equation with rational coefficients, one of whose roots is $3 plus square root of 5$ .

If the sum of the roots of the equation kx² – 3x + 9 = 0 is $3 over 11$ , then find the product of the roots of that equation.

If the sum of the roots of the equation kx² – 3x + 9 = 0 is $3 over 11$ , then find the product of the roots of that equation.

Discuss the nature of the roots of the equation 4x² – 2x + 1 = 0.

Discuss the nature of the roots of the equation 4x² – 2x + 1 = 0.

Find the roots of the equation 4x² – 13x + 10 = 0

Find the roots of the equation 4x² – 13x + 10 = 0

Find the values of k for each of the following quadratic equations, so that they have two equal roots. 2x² + kx + 3 = 0

Find the values of k for each of the following quadratic equations, so that they have two equal roots. 2x² + kx + 3 = 0