Question

The roots of the quadratic equation $x^2+(p+q)x+pq=0$ are $x=$

• A. $2p,2q$
• B. $-p,-q$
• C. $p,q$

Answer 1

The correct option is B $-p,-q$

Given: $x^2+(p+q)x+pq=0$
Let's use the factorization method for finding the roots of the equation.

Now, we will split the middle term or coefficient of $x$ in such a way that the product of these two terms is equal to the product of the constant and the coefficient of $x^2.$
$\Rightarrow x^2+(p+q)x+pq=0\Rightarrow x^2+px+qx+pq=0\Rightarrow x(x+p)+q(x+p)=0\Rightarrow (x+p)(x+q)=0\Rightarrow x=-p,-q$

Hence, the roots of the equation are $-p,-q.$