Question

if alpha and beta are the zeros of the polynomial x^2 - 5x + m such that alpha - beta =1, find m
​

Answer 1

Answer:

6

Solution:

we know that

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

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

also we can write

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

hence putting the values we get

${( - 5)}^{2} - 4(m) = { (\alpha - \beta )}^{2}$

$25 - 4(m) = { (1)}^{2}$

$25 - 4m = 1$

$25 - 1= 4m$

$24= 4m$

$m = 6$