Question

The quadratic polynomial, whose zeros are 2 and 3 is
A. ${x^2} - 5x - 6$
B. ${x^2} + 5x - 6$
C. ${x^2} - 5x + 6$
D. ${x^2} + 5x + 6$

Answer 1

Hint: Here we will the use, ${x^2} - ({\text{sum of the zeros)}}x + {\text{product of zeros}}$; equation to find the quadratic equation when zeros are mentioned.

Complete step-by-step answer:
As zeros of the polynomial are given that are 2 & 3.
Therefore the required quadratic polynomial is
$
   \Rightarrow {x^2} - ({\text{sum of the zeros)}}x + {\text{product of zeros}} \to (1) \\
   \Rightarrow {x^2} - (2 + 3)x + 2 \times 3 \\
   \Rightarrow {x^2} - 5x + 6 \\
$
Hence, Option C is the correct answer.

Note: Whenever zeros of polynomials are given, use eq (1). It will help you to solve the problem quickly. Another quick method is that zeros of the polynomial when substituted in the expression results in the value 0. So, check each option by hit and trial method.