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Q.

The zeroes of the quadratic polynomial $x^{2} + 99 x + 127$ are

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a

Both positive

b

Both negative

c

One positive and one negative

d

Both equal

answer is B.

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Detailed Solution

The given polynomial is

x^{2} + 99 x + 127

.
We know that if a polynomial is of the form

a x^{2} + bx + c = 0

, then the sum of zeroes

= \frac{- b}{a}

and the product of zeroes

= \frac{c}{a}

.
Here,
Sum of zeroes

= - 99

.
Product of the zeroes

= 127

.
We know, if the product of two numbers is positive, then both the two numbers are either positive or negative.
Here, the sum of zeroes is negative and the product of zeroes is positive, therefore both the zeroes must be negative.
Thus, both the zeroes of the quadratic polynomial

x^{2} + 99 x + 127

are negative.
Hence, option 2 is correct.

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