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Question

lf the roots of the equation ax2+bx+c=0 are the same , when each of the coefficient is increased by the same quantity, then x2+x+1 is equal to

A
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B
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C
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D
2
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Solution

The correct option is B 0
Let the coefficients of the given equation be increased by k. The new equation is:
(a+k)x2+(b+k)x+(c+k)=0
Since the roots are unchanged, the coefficient of x2, x and c in the original and new equation are in proportion.
a+ka=b+kb=c+kc
a+kaa=b+kbb=c+kcc
ka=kb=kc
a=b=c
The original equation becomes ax2+ax+a=0
x2+x+1=0
Ans- Option B

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