Question

If the two zeros of the polynomial x^3 – 9x^2 -x + 9, are 1 and 9, then the third zero is ________

(a) 9

(b) 1

(c) 2

(d) -1

The question was asked during an interview for a job.

My doubt stems from Zeros and Coefficients of Polynomial topic in division Polynomials of Mathematics – Class 10

Answer 1

Right answer is (d) -1

The best I can explain: The given polynomial is x^3 – 9x^2 – x + 9.

The two zeros of the polynomial are 1 and 9.

We know that, the sum of zeros of the polynomial or α + β + γ = \(\frac {-coefficient \, of \, x^2}{coefficient \, of \, x^3} = \frac {9}{1}\)

1 + 9 + γ =  9

γ = 9 – 10 = -1