Question

If sum of the roots of a quadratic equation is $-4$ and their product is $3$, then the quadratic equation and the roots respectively are

• A. $x^2+4x+3=0$ and $(-3,-1)$
• B. $x^2+4x+3=0$ and $(3,1)$
• C. $x^2-4x+3=0$ and $(3,1)$
• D. $x^2+4x-3=0$ and $(-3,-1)$

Answer 1

The correct option is A $x^2+4x+3=0$ and $(-3,-1)$

Given, sum of the roots of a quadratic equation is $-4$ and their product is $3$
We know that the quadratic equation is given as
$x^2-\text{(Sum of the roots)}x+\text{(product of the roots)}=0$
$\Rightarrow x^2-(-4)x+3=0$
$\Rightarrow x^2+4x+3=0\Rightarrow (x+3)(x+1)=0$
$\Rightarrow x=-3,-1$
Hence, the equation is $x^2+4x+3=0$ and its roots are $-3,-1$