Question

One root of x2 - 9x + k = 0 is twice the other.Quantity a quantity bk 27

Answer 1

p(x)=x^2-9x+k=0
given that one zero is twice the other
$\alpha + \beta = \frac{ - b}{a}$
$\alpha + 2 \alpha = 9$
$3 \alpha = 9$
$\alpha = 3$
Also,


$\alpha \beta = \frac{c}{a}$
$\alpha \times 2 \alpha = k$

${2 \alpha }^{2} = k$
Put alpha=3
$2 \times {3}^{2} = k$
$2 \times 9 = k$
$k = 18$
So, value of k=18

Hope it helps you:)