AP EAMCET · Maths · Quadratic Equation
If \(f(x)=2 x^4-13 x^2+a x+b\) is divisible by \(x^2-3 x+2\), then \((a, b)\) is equal to
- A \((-9,-2)\)
- B \((6, 4)\)
- C \((9, 2)\)
- D \((2, 9)\)
Answer & Solution
Correct Answer
(C) \((9, 2)\)
Step-by-step Solution
Detailed explanation
Given, \(f(x)=2 x^4-13 x^2+a x+b\) is divisible by \(\begin{aligned} & (x-2)(x-1) . \\ & \therefore \quad f(2)=2(2)^4-13(2)^2+a(2)+b=0 \end{aligned}\) ⇒ \(a+b=11 ...(ii)\) On solving Eqs. (i) and (ii), we get \(a=9, b=2\)
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