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NDA 2010
Exam
NDA
Year
2010
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2010 · Mathematics · Quadratic Equation

If α and β are the roots of the equation x^2-2 x+4=0 , then what is...

If α\alpha and β\beta are the roots of the equation x2−2x+4=0x^2-2 x+4=0, then what is the value of α3+β3\alpha^3+\beta^3 ?

Options

  1. A16
  2. B-16
  3. C8
  4. D-8

Correct answer

B. -16

Step-by-step solution

\alpha^3+\beta^3=(\alpha+\beta)^3-3 \alpha \beta(\alpha+\beta) \left\lvert\, since α+β=2αβ=4\begin{aligned} & \text{ since } \\ & \alpha+\beta=2 \\ & \alpha \beta=4\end{aligned}\right.=(2)3−3×4(2)=8−24=−16\begin{aligned} & =(2)^3-3 \times 4(2) \\ & =8-24 \\ & =-16\end{aligned}$$
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