if x 2 1 is a factor of x 4 ax 3 3x b then 651021254

If $${x^2} - 1$$ is a factor of $${x^4} + a{x^3} + 3x - b$$ then

A. $$a = 3, b = - 1$$

B. $$a = - 3, b = 1$$

C. $$a = 3, b = 1$$

D. None of these

Answer : $$a = - 3, b = 1$$

Solution :
Let $$f\left( x \right) = {x^4} + a{x^3} + 3x - b.\,{\text{Then }}f\left( 1 \right) = 0,f\left( { - 1} \right) = 0.$$

Releted MCQ Question on
Algebra >> Quadratic Equation

Releted Question 1

If $$\ell ,m,n$$ are real, $$\ell \ne m,$$ then the roots by the equation: $$\left( {\ell - m} \right){x^2} - 5\left( {\ell + m} \right)x - 2\left( {\ell - m} \right) = 0$$ are

A. Real and equal

B. Complex

C. Real and unequal

D. None of these

View Answer

Releted Question 2

The equation $$x + 2y + 2z = 1{\text{ and }}2x + 4y + 4z = 9{\text{ have}}$$

A. Only one solution

B. Only two solutions

C. Infinite number of solutions

D. None of these

View Answer

Releted Question 3

Let $$a > 0, b > 0$$ and $$c > 0$$ . Then the roots of the equation $$a{x^2} + bx + c = 0$$

A. are real and negative

B. have negative real parts

C. both (A) and (B)

D. none of these

View Answer

Releted Question 4

Both the roots of the equation $$\left( {x - b} \right)\left( {x - c} \right) + \left( {x - a} \right)\left( {x - c} \right) + \left( {x - a} \right)\left( {x - b} \right) = 0$$ are always

A. positive

B. real

C. negative

D. none of these.

View Answer

If $${x^2} - 1$$ is a factor of $${x^4} + a{x^3} + 3x - b$$ then

Releted MCQ Question on
Algebra >> Quadratic Equation

If $$\ell ,m,n$$ are real, $$\ell \ne m,$$ then the roots by the equation: $$\left( {\ell - m} \right){x^2} - 5\left( {\ell + m} \right)x - 2\left( {\ell - m} \right) = 0$$ are

The equation $$x + 2y + 2z = 1{\text{ and }}2x + 4y + 4z = 9{\text{ have}}$$

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Both the roots of the equation $$\left( {x - b} \right)\left( {x - c} \right) + \left( {x - a} \right)\left( {x - c} \right) + \left( {x - a} \right)\left( {x - b} \right) = 0$$ are always

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If $${x^2} - 1$$ is a factor of $${x^4} + a{x^3} + 3x - b$$ then

Releted MCQ Question on Algebra >> Quadratic Equation

If $$\ell ,m,n$$ are real, $$\ell \ne m,$$ then the roots by the equation: $$\left( {\ell - m} \right){x^2} - 5\left( {\ell + m} \right)x - 2\left( {\ell - m} \right) = 0$$ are

The equation $$x + 2y + 2z = 1{\text{ and }}2x + 4y + 4z = 9{\text{ have}}$$

Let $$a > 0, b > 0$$ and $$c > 0$$ . Then the roots of the equation $$a{x^2} + bx + c = 0$$

Both the roots of the equation $$\left( {x - b} \right)\left( {x - c} \right) + \left( {x - a} \right)\left( {x - c} \right) + \left( {x - a} \right)\left( {x - b} \right) = 0$$ are always

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