CAT Quantitative Aptitude Questions | CAT Algebra - Polynomials questions

CAT Questions | Algebra | Polynomials - Polynomial Remainder Theorem

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

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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.

 


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