(a) If α, β are the zeroes of polynomial $p(x)=6x^2-5x-3$, then fin...

Question

(a) If α, β are the zeroes of polynomial $p(x)=6x^2-5x-3$, then find the value of $\frac1\alpha+\frac1\beta$.
OR
(b) One zero of the polynomial $4x^2-12x+(2k+1)$ is five times the other. Find the value of k.

Accepted Answer

**(a)** $\alpha+\beta=\frac56$, $\alpha\beta=\frac{-3}{6}=-\frac12$. $$\frac1\alpha+\frac1\beta=\frac{\alpha+\beta}{\alpha\beta}=\frac{5/6}{-1/2}=-\frac53$$

**(b)** Let zeroes be $r$ and $5r$. Sum $=6r=\frac{12}{4}=3 \Rightarrow r=\frac12$. Product $=5r^2=\frac{2k+1}{4}$. $$5	imes\frac14=\frac{2k+1}{4} \Rightarrow 5=2k+1 \Rightarrow k=2$$

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