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The zeroes of the polynomial $x 2 + 99 x + 127$ are

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Both positive

Both negative

Both equal

One positive and one negative

answer is B.

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Detailed Solution

The given polynomial is,

x 2 + 99 x + 127

α and β

are the zeroes of

p (x) = a x 2 + b x + c,

, then

α + β = − b a and α β = c a

For quadratic polynomial

x 2 + 99 x + 127,

we have,

α + β = − 99

α β = c a

If the sum of two numbers is negative and their product is positive then both numbers must be negative.

∵ Discriminant = b 2 − 4 a c = 992 − 4 (127) = 9293 > 0

This shows that both the zeroes are real and distinct, also the sum is negative and the product is positive, therefore both the zeroes are negative.
So, option (2) is correct.

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