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If one of the zeroes of the polynomial $x 2 − 4 x + 1$ is $(2 + 3)$ , then find the other zero.

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2 − 3

2 − 7

answer is A.

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Detailed Solution

Given that one of the zeros of polynomial

x 2 − 4 x + 1

(2 + 3)

.
The relation between the zeros, say

α

and

β

, and the coefficients of a quadratic polynomial

a x 2 + b x + c

is given as follows,

α + β = − b a α β = c a

If we assume

α = (2 + 3)

as one zero and the other as

β

, then we have,

α + β = − b a 2 + 3 + β = − b a ........ (i)

Now, comparing the coefficients of the given quadratic polynomial i.e.,

x 2 − 4 x + 1

with

a x 2 + b x + c

, we have a = 1, b = – 4 and c = 1.
Substituting these values in the equation (i) and simplifying, we get,

2 + 3 + β = − (− 4) 1 2 + 3 + β = 4 β = 4 − 2 − 3 β = 2 − 3

So, the value of the other root is obtained as

2 − 3

.
Hence, the correct option is (1).

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