Question

p and q are the zeroes of the polynomial 2x^2+5x-1, find the value of p+q+pq

Answer 1

$\red{\underline{\underline{\sf{Given:}}}}$

p and q are zeroes of the polynomial $\pink{\sf{P(x) = 2x^{2}+5x-1,}}$.

$\red{\underline{\underline{\sf{To \:\:be\:\:found-}}}}$

The value of $\boxed{\bf{p+q+pq}}$

So,

a = 2, b = 5 and x = (-1)

We know that

$\boxed{\bf Sum\:\:of\:\:zeroes=-\bigg( \frac{ coefficient\:\:of\:\:x}{coeficient\:\:of\:\:x^{2}} \bigg) = \frac{-b}{a} }$

and

$\boxed{\bf Sum\:\:of\:\:zeroes=\bigg( \frac{ constant\:\:term}{coeficient\:\:of\:\:x^{2}} \bigg) = \frac{c}{a} }$

Now,

sum of zeroes,

$\bf p+q = \dfrac{-b}{a} = \dfrac{-(5)}{2}$

and

product of zeroes,

$\bf pq = \dfrac{c}{a} = \dfrac{-1}{2}$

so,

$\bf (p+q)+pq = \dfrac{-5}{2} + \dfrac{-1}{2} \\ \\ = \boxed{ \bf \dfrac{-6}{2}} = -3$

Hence,

The value of p+q+pq = -3