Question

If two of the zeros of the polynomial f(x)=x^3+(6-√3)x^2+(-1-√3)x+30-6√3 are 3 and -2 then, the other zero will be ____________

(a) -√3

(b) 5

(c) 5-√3

(d) 5+√3

This question was posed to me by my school principal while I was bunking the class.

Asked question is from Division of Polynomial in portion Polynomials of Mathematics – Class 10

Answer 1

Correct choice is (c) 5-√3

To explain I would say: Since the zeros of the polynomial are 3 and -2.

The divisor of the polynomial will be (x-3) and (x+2).

Multiplying (x-3) and (x+2) = x^2+2x-3x-6=x^2-x+6

Dividing, x^3+(6-√3)x^2+(-1-√3)x+30-6√3 by x^2-x+6

We get, x-5+√3 as quotient.

Hence, the third zero will be 5-√3.