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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2013 · Mathematics · Quadratic Equation

If the roots of a quadratic equation a x^2+b x+c=0 are α and β ,...

If the roots of a quadratic equation ax2+bx+c=0a x^2+b x+c=0 are α\alpha and β\beta, then the quadratic equation having roots α2\alpha^2 and β2\beta^2 is

Options

  1. Ax2−(b2−2ac)x+c=0x^2-\left(b^2-2 a c\right) x+c=0
  2. Ba2x2−(b2−2ac)x+c=0a^2 x^2-\left(b^2-2 a c\right) x+c=0
  3. Cax2−(b2−2ac)x+c2=0a x^2-\left(b^2-2 a c\right) x+c^2=0
  4. Da2x2−(b2−2ac)x+c2=0a^2 x^2-\left(b^2-2 a c\right) x+c^2=0

Correct answer

D. a2x2−(b2−2ac)x+c2=0a^2 x^2-\left(b^2-2 a c\right) x+c^2=0

Step-by-step solution

Required equation is x2−x(α2+β2)+(αβ)2=0x2−x[(α+β)2−2αβ]+(αβ)2=0x^2-x\left(\alpha^2+\beta^2\right)+(\alpha \beta)^2=0x^2-x\left[(\alpha+\beta)^2-2 \alpha \beta\right]+(\alpha \beta)^2=0x2−x(b2a2−2ca)+c2a2=0⇒a2x2−x(b2−2ac)+c2=0\begin{aligned} & x^2-x\left(\frac{b^2}{a^2}-\frac{2 c}{a}\right)+\frac{c^2}{a^2}=0 \\ & \Rightarrow \quad a^2 x^2-x\left(b^2-2 a c\right)+c^2=0\end{aligned}$$
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