CAT Quantitative Aptitude Questions | CAT Algebra - Polynomials questions

The question is about Polynomial Remainder Theorem. This can be solved by substituting all the values in the given equation. As simple as that!! Polynomials is a simple topic which involves a lot of basic ideas. Make sure that you a get of hold of them by solving these questions. A range of CAT questions can be asked based on this simple concept.

Question 3: x⁴ – ax³ + bx² – cx + 8 = 0 divided by x – 1 leaves a remainder of 4, divided by x + 1 leaves remainder 3, find b.

1. 2.5
2. -5.5
3. 3.5
4. 6.5

Video Explanation

Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Polynomials: This can be solved by substituting all the values in the given equation. As simple as that!!

Let f(x) = x⁴ – ax³ + bx² – cx + 8

f(1) = 4
1 – a + b – c + 8 = 4
–a + b – c = - 5 ...... Eqn (1)
f(–1) = 3
1 + a + b + c + 8 = 3
a + b + c = - 6 ...... Eqn (2)
Adding Equation (1) and (2) we have
2b = -11,
or b = -5.5

The question is "x⁴ – ax³ + bx² – cx + 8 = 0 divided by x – 1 leaves a remainder of 4, divided by x + 1 leaves remainder 3, find b."

Hence the answer is "-5.5"

Choice B is the correct answer.