Question

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

Answer 1

Answer:

$x^2 + 3x + 1 = 0$

Step-by-step explanation:

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

• Given equation is

        $x^2 +5x +5=0$ ----------------- eq1

• 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 =$\frac{-b}{a} = \frac{-5}{1} = -5$ ${\boxed {\boxed{-5{ {\ }}}}}$

        product of roots = αβ = $\frac{c}{a} = \frac{5}{1} =5$  ${\boxed {\boxed{5{ {\ }}}}}$

• 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