If f(x)={bx2−a;x<−1ax2−bx−2;x≥−1 If f and f′ are continuous everywhere, then the equation whose roots are a and b is:
A
x2+3x−2=0
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B
x2−3x+2=0
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C
x2+3x+2=0
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D
x2−3x−2=0
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Solution
The correct option is Bx2−3x+2=0 f(x)={bx2−a;x<−1ax2−bx−2;x≥−1 ∵f(x) is a continuous function ∴f(−1−)=f(−1+)=f(−1) ⇒b−a=a+b−2 ⇒a=1 f′(x)={2bx;x<−12ax−b;x>−1 ∵f′(x) is continuous everywhere, ∴f′(−1−)=f′(−1+)=f′(−1) ⇒−2b=−2a−b ⇒b=2a ∴a=1,b=2 Equation whose roots are 1 and 2 is (x−2)(x−1)=0⇒x2−3x+2=0