Question

If alpha and beta are zeros of the polynomial x square minus 6 minus K such that Alpha minus beta equal to 9 find k

Answer 1

Answer:

$k=\dfrac{57}{4}$

Step-by-step explanation:

$Given \ p(x)=x^2-6-k \ and \ \alpha- \beta=9\\\\we \ know \ formula \ for \ sum \ and \ product \ of \ zeroes\\\\\alpha +\beta=\dfrac{-b}{a} \ where \ b \ is \ coefficient \ of \ x \ and \ a \ is \ coefficient \ of \ x^2\\\\\alpha +\beta=0\\\\For \ product\\\\\alpha \beta=\dfrac{c}{a} \ where \ c \ is \ coefficient \ of \ constant \ term.\\\\\alpha \beta=-6-k\\\\ we \ know\\\\(\alpha +\beta )^2-4\alpha \beta=(\alpha- \beta )^2\\\\\\putting \ value \ here\\\\(0)^2-4\times(-6-k)=9)^2\\\\4(6+k)=81$

$24+4k=81\\\\\\4k=81-24\\\\\\k=\dfrac{57}{4}\\\\\\Thus \ we \ get \ k=\dfrac{57}{4}.$