Question

The zeroes of the quadratic polynomial x² + 99x + 127 are

(a) both positive (b) both negative
(c) both equal (d) one positive and one negative

Answer 1

Let f(x) = x² + 99x + 127.

Product of the zeroes of f(x) = $127\times 1=127$ [Product of zeroes = $\frac{c}{a}$ when f(x) = ax² + bx + c]

Since the product of zeroes is positive, we can say that it is only possible when both zeroes are positive or both zeroes are negative.

Also, sum of the zeroes = –99 [Sum of zeroes = $-\frac{b}{a}$ when f(x) = ax² + bx + c]

The sum being negative implies that both zeroes are positive is not correct.

So, we conclude that both zeroes are negative.

Hence, the correct answer is option B.