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The zeroes of the quadratic polynomial $x 2 + k x + k, k ≠ 0$ are

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both be positive

both be negative

are always unequal

answer is A.

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Detailed Solution

Given quadratic polynomial is

x 2 + k x + k, k ≠ 0

.
We know that in quadratic polynomial

m x^{2} + nx + l = 0

,
Sum of zeroes

= \frac{- n}{m}

and product of zeroes

= \frac{c}{a}

.
On comparing given polynomial with standard form we get,

m = 1, n = k, l = k

.
Then,
Sum of zeroes

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

Since, sum is zeroes therefore one of the zeroes is negative.
And
Product of zeroes

= \frac{k}{1} = k

Since, product is positive therefore both the zeroes have same sign.
Hence, zeroes are both negative.
Therefore, option 1 is correct.

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