Question

If one zero of
f(x) = 4$\square x^2$ - 8kx + 8x - 9
is negative of the other, find zeroes of
k$\square x^2$ + 3kx + 2.

Answer 1

f(x) = 4$\square x^2$ -8kx + 8x - 9$

Let one zero be $\alpha$

and then other will be $=-\alpha$

$\Rightarrow$ Sum of zeroes $\Rightarrow \alpha -\alpha =0=\frac{(8k-8)}{4}$

$\Rightarrow k=1$

$\therefore$ Zeroes of $1{\left(x\right)}^2+3\left(x\right)x+2$

$=x^2+3x+2$

$=x^2+x+2x+2$

$=x(x+1)+2(x+1)$

$=(x+1)(x+2)$

$\therefore$ Zeroes $=x=-1,-2.$

Hence, the answer is $-1,-2.$