Question

What will be the value of other zero, if one zero of the quadratic polynomial is 5 and the sum of the zeros is 10?

(a) 10

(b) 5

(c) -5

(d) -10

The question was asked during an internship interview.

This interesting question is from Zeros and Coefficients of Polynomial topic in portion Polynomials of Mathematics – Class 10

Answer 1

Right option is (b) 5

Easiest explanation: One zero of the quadratic polynomial is 5. ∴ the factor of the polynomial is (x-5)

Let us assume the other zero to be b. ∴ the other factor of the polynomial is (x-b)

Multiplying the factors, we have (x-5)(x-b)

x^2-5x-bx+5b

x^2-(5+b)x+5b

The sum of zeros is 10.

∴ \(\frac {-coefficient \, of \, x}{coefficient \, of \, x^2}\)=10

\(\frac {-(-5-b)}{1}\)=10

5+b=10

b=5

The equation becomes x^2-10x+25.

Therefore, the other zero is 5.