Question

What will be the polynomial if its zeros are 3, -3, 9 and -9?

(a) x^4-80x^2+729

(b) x^4-90x^2+729

(c) x^4-90x^2+79

(d) x^4-100x^2+729

I got this question by my school principal while I was bunking the class.

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

Answer 1

Right option is (b) x^4-90x^2+729

To explain I would say: The zeros of the polynomial are 3, -3, 9 and -9.

Then, (x-3), (x+3), (x-9) and (x+9) are the factors of the polynomial.

Multiplying the factors, we have

(x-3) (x+3) (x-9) (x+9)

(x^2-9) (x^2-81) (By identity (x-a)(x+a)=x^2-a^2)

(x^4-9x^2-81x^2+729)

x^4-90x^2+729