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Find a quadratic polynomial whose zeroes are $4$ and $3$ .

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x 2 − 7 x + 12

5 x 2 + 9 x + 1

3 x 2 + 5 x + 10

2 x 2 − 6 x + 12

answer is B.

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Detailed Solution

Given that

4

and

3

are zeroes of a quadratic polynomial. We need to form a quadratic polynomial.
When

α

and

β

are the zeroes of quadratic polynomial, the two equations formed with zeroes are given as:

α + β = − b a

and

α β = c a

where

b

is the coefficient of linear term,

c

is constant while

a

is the coefficient of quadratic term in quadratic polynomial.
Based on the relationship between zeroes and polynomials we have quadratic polynomial as:

f (x) = x 2 − (α + β) x + α β ... (i)

where

α & β

are the zeroes of the polynomial.
Now we have,
Sum of zeroes,

α + β = 4+3 ⇒ α + β = 7

and
Product of zeroes,

α β = 4 × 3 α β = 12

Now equating the value of

α + β

and

α β

in equation

(i)

, we have,

f (x) = x 2 − 7 x + 12

Hence, the value of the quadratic polynomial is

x 2 − 7 x + 12

.
Therefore, option 2 is correct.

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