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Find a quadratic polynomial whose zeroes are $3 + 2$ and $3 − 2$ .

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x 2 − 6 x + 7 = 0

x 2 + 6 x − 7 = 0

2 x 2 − 7 x + 6 = 0

2 x 2 + 6 x − 7 = 0

answer is A.

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Detailed Solution

Given that the zeroes of a polynomial are

3 + 2

and

3 − 2

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

a x 2 + b x + c = 0.

A quadratic polynomial with zeroes

α

and

β

is given as,

x − α x − β = 0 ... (i)

We have,

α = 3 + 2

β = 3 − 2

Equating the values in equation

(i)

, we have,

x − 3 + 2 x − 3 − 2 = 0 ⇒ x 2 − 3 + 2 x − 3 − 2 x + 32 − 22 = 0 ⇒ x 2 − 6 x + 9 − 2 = 0 ∴ x 2 − 6 x + 7 = 0

Hence, the quadratic polynomial is

x 2 − 6 x + 7 = 0

.
Therefore, option 1 is correct.

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