MHT CET · Maths · Quadratic Equation
If \(\mathrm{f}(x)=2 x^3+\mathrm{m} x^2-13 x+\mathrm{n}\) and 2,3 are the roots of the equation \(\mathrm{f}(x)=0\) then the value of \(4 \mathrm{~m}+5 \mathrm{n}\) is
- A \(30\)
- B \(100\)
- C \(130\)
- D \(150\)
Answer & Solution
Correct Answer
(C) \(130\)
Step-by-step Solution
Detailed explanation
\(2(2)^3 + m(2)^2 - 13(2) + n = 0 \Rightarrow 16 + 4m - 26 + n = 0 \Rightarrow 4m + n = 10\) \(2(3)^3 + m(3)^2 - 13(3) + n = 0 \Rightarrow 54 + 9m - 39 + n = 0 \Rightarrow 9m + n = -15\)
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