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Find the quadratic polynomial whose sum and product of the zeroes are $218$ and $516$ respectively.

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16 x 2 − 42 x + 5 = 0

8 x 2 − 32 x + 10 = 0

− 9 x 2 − 41 x + 7 = 0

6 x 2 − 21 x + 5 = 0

answer is A.

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Detailed Solution

Given that the sum and product of the zeroes of a polynomial are

218

and

516

respectively. We need to find the quadratic polynomial.
General form of quadratic polynomial is given as:

a x 2 + b x + c = 0.

Let us assume the zeroes of the polynomial be

α & β .

Based on the relationship between zeroes and polynomials we have quadratic polynomial as:

p (x) = x 2 − (α + β) x + α β ..... (i)

Now we have,

α + β = 218

α β = 516

Equating the values in equation (i) we have,

p (x) = x 2 − 218 x + 516 ⇒ p (x) = 16 x 2 − 42 x + 5 16

Now equating

p (x) = 0

we have,

16 x 2 − 42 x + 5 = 0

Hence, the quadratic polynomial is

16 x 2 − 42 x + 5 = 0.

Therefore, option 1 is correct.

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