Question

If a and ẞ are the zeros of the polynomial f(x) = x ^ 2 - 5x2 + k , where alpha - beta = 1 , then k is
please give correct answer​

Answer 1

Answer:

${x}^{2} - 5 \times 2 + k = 0$

${x}^{2} - 10 + k = 0$

${ x}^{2} + 0 x - 10 + k = 0$

$comparing \: with \: a {x}^{2} + bx + c = 0$

$a = 1$

$b = 0$

$c = - 10 + k$

$\alpha \: and \: \beta \: are \: the \: zeros \: of \: the \: equation$

$\alpha + \beta = \frac{ - b}{a}$

$\alpha + \beta = \frac{ - 0}{1}$

$\alpha + \beta = 0$

$\alpha \times \beta = \frac{c}{a}$

$\alpha \times \beta = \frac{ - 10 + k}{1}$

$\alpha \times \beta = - 10 + k$

${( \alpha - \beta )}^{2} = {( \alpha + \beta )}^{2} - 4 \alpha \beta$

$since$

$\alpha - \beta = 1$

$therefore$

${1}^{2} = {0}^{2} - 4( - 10 + k)$

$1 = - 40 + 4k$

$4k = 1 + 40$

$k = \frac{41}{4}$