Q47 / 120 · VITEEE 2009 · Mathematics

If $f(x)=2 x^{4}-13 x^{2}+a x+b$ is divisible by $\mathrm{x}^{2}-3 x+2$, then $(a, b)$ is equal to

  • A
    $(-9,-2)$
  • B
    $(6,4)$
  • Correct answer
    C
    $(9,2)$
  • D
    $(2,9)$

Solution

$$ \begin{array}{l} f(x)=2 x^{4}-13 x^{2}+a x+b \text { is divisible by } \\ (x-2)(x-1) \\ \therefore f(2)=2(2)^{4}-13(2)^{2}+a(2)+b=0 \\ \Rightarrow 2 a+b=20...(i) \end{array} $$ $$ \begin{array}{l} \text { and } f(1)=2(1)^{4}-13(1)^{2}+a+b=0 \\ \Rightarrow a+b=11...(ii) \end{array} $$ On solving Eqs. (i) and (ii), we get $a=9, b=2$

Hence, the correct answer is option: 'C'.

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