Question

The zeroes of the quadratic polynomial x² + ax + a, $a\ne 0,$

(a) cannot be both positive (b) cannot both be negative

(c) are always unequal (d) are always equal

Answer 1

Let f(x) = x² + ax + a.
Product of the zeroes of f(x) = a [Product of zeroes = $\frac{c}{a}$ when f(x) = ax² + bx + c]
Since the product of zeroes is positive, so the zeroes must be either both positive or both negative.
Also, sum of the zeroes = –a [Sum of zeroes = $-\frac{b}{a}$ when f(x) = ax² + bx + c]
So, the sum of the zeroes is negative, so the zeroes cannot be both positive.

Hence, the correct answer is option B.