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Question

Let f(x) be a quadratic expression such that f(0+f(1)=0. If f(−2)=0, then

A
f(25)=0
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B
f(25)=0
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C
f(35)=0
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D
f(35)=0
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Solution

The correct option is C f(35)=0
Let the quadratic expression be, f(x)=ax2+bx+c

f((0)+f(1)=0a+b+2c=0(1)

f(2)=04a2b+c=0(2)

2×(1)+(2), we get 6a+5c=0c=6a5

2×(2)(1), we get 7a5b=0b=7a5

f(x)=ax2+7a5x6a5

f(x)=a(x2+7x565)

f(x)=a(x35)(x+2)

f(35)=0

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