Mathematics

Quadratic-Equations

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

8ac = 25b
8ac = 9b²
8b² = 9ac
8b² = 25ac

The correct answer is: 8b² = 25ac

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 _____.

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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

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

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

8ac = 25b8ac = 9b28b2 = 9ac8b2 = 25ac

The correct answer is: 8b2 = 25ac

Related Questions to study

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.

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.

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

8ac = 25b
8ac = 9b²
8b² = 9ac
8b² = 25ac

The correct answer is: 8b² = 25ac

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.

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.