NDA 2019 Maths · Mathematics · Quadratic Equations · medium

If α,β are the roots of x^2-5x+3=0, the equation whose roots are α+1 and β+1 is

Single correct option

\alpha,\beta

are the roots of

x^2-5x+3=0

, the equation whose roots are

\alpha+1

and

\beta+1

Show answer and solution

Answer: (C) $x^2-7x+9=0$

The new roots are

\alpha+1,\beta+1

, so their sum is

5+2=7

and their product is

\alpha\beta+(\alpha+\beta)+1=3+5+1=9

. The equation is

x^2-7x+9=0

. Equivalently substitute

x-1

for

x

in the original equation. Keeping the old product

3

is the common slip, as the product changes when each root is shifted.

Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake