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Question

If f(x)={bx2a;x<1ax2bx2;x1
If f and f are continuous everywhere, then the equation whose roots are a and b is:

A
x2+3x2=0
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B
x23x+2=0
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C
x2+3x+2=0
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D
x23x2=0
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Solution

The correct option is B x23x+2=0
f(x)={bx2a;x<1ax2bx2;x1
f(x) is a continuous function
f(1)=f(1+)=f(1)
ba=a+b2
a=1
f(x)={2bx;x<12axb;x>1
f(x) is continuous everywhere,
f(1)=f(1+)=f(1)
2b=2ab
b=2a
a=1,b=2
Equation whose roots are 1 and 2 is
(x2)(x1)=0x23x+2=0

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