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If both the zeroes of the quadratic polynomial $a x 2 + b x + c, c ≠ 0$ are equal, then which of the subsequent is correct?

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c and a

have opposite signs

c and b

have opposite signs

c and a

have same signs

c and b

have same signs

answer is C.

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Detailed Solution

Given that both the zeroes of the quadratic polynomial

a x 2 + b x + c, c ≠ 0

are equal.
If both the zeroes of the quadratic polynomial

a x 2 + b x + c, c ≠ 0

are equal, then

b 2 = 4 a c .

⇒ a c = b 2 4

Due to the fact that the square of any real number is always positive,

b 2

is always positive.
This shows that the product

a c

must be positive.
Since the product

a c

is positive, therefore the two numbers

c and a

must be of the same sign.
Hence, option (3) is correct.

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