Question

One
Zero Of the Quadratic polynomice
x² + 3x+k is 2
then the value of k​

Answer 1

$let \: \alpha \: and \: \beta \: be \: the \: zeroes \: of \: the \: polynomial \: f(x) = {x}^{2} + 3x + k. \: then$

$\alpha + \beta = - ( \frac{3}{1} ) \: = - 3 \: and \: \alpha \beta = \frac{k}{1} = k$

$it \: is \: given \: that$

${ \alpha }^{2} + { \beta }^{2} = 2$

$( { \alpha + \beta })^{2} - 2 \alpha \beta = 2$

$( { - 3})^{2} - 2k = 2$

$9 - 2k = 2 \\ 9 - 2 = 2k \\ 7 = 2k \\ 2k = 7 \\ k = \frac{7}{2} \\ k = 3.5 \\ ( \alpha + \beta = - 3 \: and \: \alpha \beta = k)$

I hope it is helpful answer for you