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Question

If the zeros of the polynomial x33x2+x+1 are ab,a,a+b, then the value of a+b is

A
2+1
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B
12
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C
31
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D
Either a or b
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Solution

The correct options are
B 2+1
C 12
Comparing the given polynomial x33x2+x+1 with Ax3+Bx2+Cx+D. we get
A=1,B=3,C=1,D=1
Here, the zeros of the given polynomial are ab,a,a+b.
Sum of zeros=BA=31=3
ab+a+a+b=3.
3a=3.
a=1.

Product of zeros=DA=11=1

(ab)(a)(a+b)=1.
a(a2b2)=1.
since, a=1
(12b2)=1.
b2=2
b=2 or 2
value of a+b=2+1 or 12

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