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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2022 · Mathematics · Quadratic Equation

Let α and β be the roots of the equation x^2-a x-b x+a b-c=0 . What...

Let α\alpha and β\beta be the roots of the equation x2−ax−bx+ab−c=0x^2-a x-b x+a b-c=0. What is the quadratic equation whose roots are aa and bb ?

Options

  1. Ax2−αx−βx+αβ+c=0x^2-\alpha x-\beta x+\alpha \beta+c=0
  2. Bx2−αx−βx+αβ−c=0x^2-\alpha x-\beta x+\alpha \beta-c=0
  3. Cx2+αx+βx+αβ+c=0x^2+\alpha x+\beta x+\alpha \beta+c=0
  4. Dx2+αx+βx+αβ−c=0x^2+\alpha x+\beta x+\alpha \beta-c=0

Correct answer

A. x2−αx−βx+αβ+c=0x^2-\alpha x-\beta x+\alpha \beta+c=0

Step-by-step solution

Given that α\alpha and β\beta are roots of the equation x2−ax−bx+ab−c=0 i.e x2−(a+b)x+ab−c=0∴α+β=a+bα.β=ab−c⇒ab=αβ+c\begin{array}{cl} & x^2-a x-b x+a b-c=0 \\ \text{ i.e } & x^2-(a+b) x+a b-c=0 \\ \therefore & \alpha+\beta=a+b \quad \alpha . \beta=a b-c \\ \Rightarrow & a b=\alpha \beta+c\end{array} The quadratic equation whose roots are aandba and b is x2−(a+b)x+ab=0x2−(α+β)x+αβ+c=0x2−\alphax−\betax+αβ+c=0\begin{aligned}& x²-(a+b) x+a b=0 \\ & x²-(\alpha+\beta)x+\alpha \beta+c=0 \\ & x²-\alphax-\betax+\alpha \beta+c=0\end{aligned}
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