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Question

Find the quadratic polynomial whose zeroes are 6+33 and 633 .


A

x216x+9

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B

3x212x+11

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C

6x24x+1

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D

7x24x+11

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Solution

The correct option is B

3x212x+11


Let α & β be the roots.
Sum of zeroes, α+β=6+33+633 =123=4

Product of zeroes, αβ=6+33×633=62(3)29αβ=3639=339=113

Required polynomial f(x)=[(x2(α+β)x+(αβ)] =[(x24x+113]

Multiplying by 3

f(x)=3x212x+11

the required polynomial is 3x212x+11.


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