Question

Find the sum of the roots of the quadratic equation $x^2-7x+12=0.$

• A. 7

Answer 1

The correct option is A 7
Consider the quadratic equation $x^2-7x+12=0.$
Comparing the given quadratic equation with the standard form $a{x}^2+bx+c=0,$ where $a,b$ and $c$ are constants ($a\ne 0$),
$\Rightarrow a=1,b=-7$ and $c=12.$
$a\times c=1\times 12=12$
$b=-7=-4+(-3)$
$\therefore x^2-7x+12=0⟹x^2-4x-3x+12=0$
$\Rightarrow x(x-4)-3(x-4)=0$
$\Rightarrow (x-4)(x-3)=0$
$\Rightarrow x=4,3$ are the roots of the equation.

Hence, the sum of the roots of the given equation is 4 + 3 = 7.