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Question

Find a quadratic polynomial with 18 as the sum and 2 as product of its zeroes.


A

8x2+x+16

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B

8x2x+16

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C

8x2x16

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D

8x2+x16

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Solution

The correct option is B

8x2x+16


Let, α & β be zeroes.
Given, α+β=18; αβ=2
Therefore required polynomial is p(x)=k[x2(α+β)x+αβ] where k is a real number.

Now, consider p(x)=k[x218x+2]

p(x)=k[8x2x+168]

p(x)=k×18[8x2x+16]

Let's take k = 8

(Note: multiplying a polynomial with a non-zero constant doesn't change the zeroes of the polynomial).

p(x)=8x2x+16

Therefore, (8x2x+16) is a polynomial with 18 as the sum and 2 as product of its zeroes.


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