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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