Question

if alpha and beta are roots of equation x2+5x+5=0 then write quadratic equation whose roots are alpha+1 and beta+1

Answer 1

x= A(alpha) , x= B(beta)
to find.
x= (A+1) , x=B+1
from this,
A= x-1 , B =x-1
now put it in place of x in the given equation.
x^2+5x+5=0
(x-1)^2+5(x-1) +5 =0

Answer 2

The quadratic equation whose roots are α + 1, β + 1 is $x^{2}$ + 3x + 1 = 0

• Given equation is

           $x^{2} + 5x + 5 = 0$        ---------------(1)

• Comparing with $ax^{2} + bx + c = 0$ , we get

           a = 1, b = 5, c = 5

• Roots of (1) are α, β

           sum of roots = α + β = $\frac{-b}{a} = \frac{-5}{1}$ = -5 -----------(2)

           product of roots = αβ = $\frac{c}{a} = \frac{5}{1}$ = 5  -------------(3)

• Quadratic equation with roots α + 1, β + 1 is given by

             $x^{2}$ - (sum of roots)x + (product of roots) = 0

             $x^{2}$ - (α + 1 + β + 1)x + (α+1)(β+1) = 0

             $x^{2}$ - (α + β + 2)x + αβ + α + β + 1 = 0

             $x^{2}$ - (-5+2)x + 5 + (-5) + 1 = 0       [from (2) and (3)]

             $x^{2}$ - (-3)x + 5 - 5 + 1 = 0

             $x^{2}$ + 3x + 1 = 0