The zeros of the quadratic polynomial

Question:

The zeros of the quadratic polynomial $x^{2}+88 x+125$ are

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

 

Solution:

(b) both negative

Let $\alpha$ and $\beta$ be the zeroes of $x^{2}+88 x+125$.

Then $\alpha+\beta=-88$ and $\alpha \times \beta=125$

This can only happen when both the zeroes are negative.

 

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