# For what value of

Let the two polynomials be,

P(x) = ax3 + 3x2 – 3 …(i)

Q(x) = 2x3 – 5x + a …(ii)

Now, we understand by the question that,

P(x) and Q(x) divided by (x – 4) gives the same remainder.

We need to find zero of the linear polynomial, (x – 4).

To find zero, put (x – 4) = 0

x – 4 = 0

x = 4

By Remainder theorem that says, f(x) is a polynomial of degree n (n ≥ 1) and ‘a’ is any real number. If f(x) is divided by (x – a), then the remainder will be f(a).

Here, a = 4.

This means, remainder when P(x) is divided by (x – 4) is P(4).

Remainder = P(4)

Remainder = a(4)3 + 3(4)2 – 3

Remainder = 64a + 48 – 3

Remainder = 64a + 45 …(iii)

And remainder when Q(x) is divided by (x – 4) is Q(4).

Remainder = Q(4)

Remainder = 2(4)3 – 5(4) + a

Remainder = 128 – 20 + a

Remainder = 108 + a …(iv)

When P(x) and Q(x) are divided (x – 4) , they leave same remainder.

Comparing equations (iii) and (iv), we have

64a + 45 = 108 + a

64a – a = 108 – 45

63a = 63

a = 1

Thus, a = 1.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :

By applying RemaiWest Bengal Mathematics

By applying RemaiWest Bengal Mathematics

By applying RemaiWest Bengal Mathematics

By applying RemaiWest Bengal Mathematics

By applying RemaiWest Bengal Mathematics

If the polynomialWest Bengal Mathematics

Let us show that West Bengal Mathematics

Let us show that West Bengal Mathematics

Let us show that West Bengal Mathematics

If the polynomialWest Bengal Mathematics