AP EAMCET · Maths · Quadratic Equation
If \(x^2+x-6\) is a factor of \(2 x^3+x^2+a x+b\), then \(6 a+13 b=\)
- A \(305\)
- B \(133\)
- C \(0\)
- D \(-1\)
Answer & Solution
Correct Answer
(C) \(0\)
Step-by-step Solution
Detailed explanation
Since, \(x^2+x-6=0\) \(\Rightarrow(x+3)(x-2)=0 \Rightarrow x=-3,2\) So, \(2(-3)^3+(-3)^2+a(-3)+b=0\) \(\Rightarrow-3 \mathrm{a}+\mathrm{b}=45\) ... (i) and \(2(2)^3+(2)^2+2 a+b=0\) \(\Rightarrow 2 \mathrm{a}+\mathrm{b}=-20\) ... (ii) After solving (i) \& (ii) we get…
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