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# Choose the correct answer from the given four options in the following questions:

The zeroes of the quadratic polynomial $ x^{2}+k x+k, k

0 $,

**(A)** cannot both be positive

**(B)** cannot both be negative

**(C)** are always unequal

**(D)** are always equal

Given:

Quadratic polynomial \( x^{2}+k x+k, k

≠ 0 \).

To do:

We have to find the nature of the zeroes.

Solution:

Let $p(x)=x^{2}+k x+k$

Here,

Product of zeroes $=\frac{\text { Constant term }}{\text { Coefficient of } x^{2}}$

$=\frac{k}{1}$

$=k$

The sign is positive it means both the zeroes should have the same sign(both positive or both negative).

Sum of zeroes $=-\frac{\text { Coefficient of } x}{\text { Coefficient of } x^{2}}$

$=-\frac{k}{1}$

$=-k$

The sign is negative and both have the same sign.

This implies, the zeroes are both negative.

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