Question

If 'p' and 'q' are the roots of the equation $2a^2-4a+1=0$. Find the value of $(p+q{)}^2+4pq$

Answer 1

We know that if $p$ and $q$ are the roots of a quadratic equation $a{x}^2+bx+c=0$, the sum of the roots is $p+q=-\frac{b}{a}$ and the product of the roots is $pq=\frac{c}{a}$.

Here, the given quadratic equation $2a^2-4a+1=0$ is in the form $a{x}^2+bx+c=0$ where $a=2,b=-4$ and $c=1$.

The sum of the roots is:

$p+q=-\frac{b}{a}=-\frac{(-4)}{2}=2$

The product of the roots is $\frac{c}{a}$ that is:

$pq=\frac{c}{a}=\frac{1}{2}$

Now,

$(p+q{)}^2+4pq=2^2+(4\times \frac{1}{2})=4+2=6$

Hence, the value of $(p+q{)}^2+4pq=6$.