Question

Which of the following quadratic function has roots – 8 and – 3?

Answer 1

Required Solution:-

the roots of the quadratic equation are- 3 and #8

Let α=3 and β=8

α+β=3+8=11 and α×β=3×8=24

The required quadratic equation is

x2−(α+β)x+α.β=0

∴ x2−11x+24=0

Answer 2

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The roots of the quadratic equation are -3 and -8,

$let \: \alpha = - 8 \: and \: \beta = - 3 \\ \alpha + \beta = ( - 8) + ( - 3) \\ \implies \: \alpha + \beta = - 11 \\ and \\ \alpha \times \beta =( - 8) \times ( - 3) \\ \implies \: \alpha \times \beta =24$

$the \: required \: quadratic \: equation \: is \: \\ {x}^{2} - ( \alpha + \beta )x + \alpha \times \beta \\ \implies{x}^{2} + 11x + 24 = 0$