Question

If p and q are the zeroes of 4 x² + 3 x + 7 then 1/p +1/q is equal to​

Answer 1

Given: $4x^{2} + 3 x + 7$

We have to find the value of$1/p +1/q$.

We know that equation$a x^{2}+b x+c=0$

Then sum of roots $=\frac{-b}{a}$   , and product of roots= $\frac{\mathrm{c}}{\mathrm{a}}$

We are solving in the following way:

We have,

$4x^{2} + 3 x + 7$

Since p and q are the zeroes.

So, from the given quadratic equation,

Then sum of roots$(p+q)=\frac{-b}{a}=\frac{-3}{4}$

and product of roots$pq$= $\frac{c}{a}$ $\Rightarrow \frac{7}{4}$

Now,

The value of$1/p +1/q$ will be:

$\begin{array}{l}\frac{1}{p}+\frac{1}{q}=\frac{p+q}{ pq} \\\\=\frac{-\frac{3}{4}}{\frac{7}{4}}=-\frac{3}{7} \\\\\Rightarrow \frac{1}{p}+\frac{1}{q}=-\frac{3}{7}\end{array}$

Hence, the value of$1/p +1/q$ will be$-\frac{3}{7}$.