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Question

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


Solution

$$f\left( x \right) =4x^2-8kx+8x-9$$
Let one zero be $$\alpha $$
and then other will be $$=-\alpha $$
$$\Rightarrow$$ Sum of zeroes $$\Rightarrow \alpha -\alpha =0=\dfrac { \left( 8k-8 \right)  }{ 4 } $$
$$\Rightarrow k=1$$
$$\therefore$$ Zeroes of $$1{ \left( x \right)  }^{ 2 }+3{ \left( x \right)  }x+2$$
$$=x^2+3x+2$$
$$=x^2+x+2x+2$$
$$=x\left( x+1 \right) +2\left( x+1 \right) $$
$$=\left( x+1 \right) \left( x+2 \right) $$
$$\therefore$$ Zeroes $$=x=-1,-2.$$
Hence, the answer is $$-1,-2.$$

Mathematics

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