Question

write the quadratic equation, alpha + beta =9 and Alpha * beta equals = 20​

Answer 1

Step-by-step explanation:

$given: \\ \alpha + \beta = 9 \\ \alpha \beta = 20 \\ a \: quadratic \: equation \: when \: sum \: \\ and \: product \: of \: roots \: are \: given \: is \: \\ given \: as : \\ {x}^{2} - ( \alpha + \beta )x + \alpha \beta = 0 \\ \implies \boxed{ {x}^{2} - 9 x + 20 = 0}$

Answer 2

The quadratic equation is $x^{2}$ - 9x + 20 = 0.

Step-by-step explanation:

We have,

α + β = 9 and αβ = 20

To find, the quadratic equation = ?

If α and β be the roots of the quadratic equation.

The quadratic equation:

$x^{2}$ - (α + β)x + αβ = 0

$x^{2}$ - 9x + 20 = 0

∴ The quadratic equation, $x^{2}$ - 9x + 20 = 0

Thus, the quadratic equation is $x^{2}$ - 9x + 20 = 0.