Let f( x ) = ax^3 + 5x^2 - bx + 1. If f( x ) when divided by 2x + 1 leaves 5 as remainder, and f'( x ) is divisible by 3x - 1 then

Use f( - 12 ) = 5andf( 13 ) = 0.

let f x ax 3 5x 2 bx 1 if f x when divided by 2x 1 leaves 5

Let $$f\left( x \right) = a{x^3} + 5{x^2} - bx + 1.$$ If $$f\left( x \right)$$ when divided by $$2x + 1$$ leaves $$5$$ as remainder, and $$f'\left( x \right)$$ is divisible by $$3x - 1$$ then

A. $$a = 26,b = 10$$

B. $$a = 24,b = 12$$

C. $$a = 26,b = 12$$

D. none of these

Answer : $$a = 26,b = 12$$

Solution :
$${\text{Use }}f\left( { - \frac{1}{2}} \right) = 5\,\,{\text{and}}\,f'\left( {\frac{1}{3}} \right) = 0.$$

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

Let $$f\left( x \right) = a{x^3} + 5{x^2} - bx + 1.$$ If $$f\left( x \right)$$ when divided by $$2x + 1$$ leaves $$5$$ as remainder, and $$f'\left( x \right)$$ is divisible by $$3x - 1$$ 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

Practice More Releted MCQ Question on
Quadratic Equation

Practice More MCQ Question on Maths Section

Let $$f\left( x \right) = a{x^3} + 5{x^2} - bx + 1.$$ If $$f\left( x \right)$$ when divided by $$2x + 1$$ leaves $$5$$ as remainder, and $$f'\left( x \right)$$ is divisible by $$3x - 1$$ 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

Practice More Releted MCQ Question on Quadratic Equation

Practice More MCQ Question on Maths Section

Releted MCQ Question on
Algebra >> Quadratic Equation

Practice More Releted MCQ Question on
Quadratic Equation