MathematicsFind roots of equation x2-11x+28=0 by quadratic formula.

Find roots of equation $x^{2} - 11 x + 28 = 0$ by quadratic formula.

A
$4, 7$
B
$- 4, - 7$
C
$4, - 7$
D
$- 4, 7$

Solution:

It is given that the quadratic equation is equation is

x^{2} - 11 x + 28 = 0

.
We have a formula for solving quadratic equation

a x^{2} + bx + c = 0

which is,

x = \frac{- b \pm \sqrt{b^{2} - 4 ac}}{2 a}

.
Substituting the values of a, b, and c from the given equation in the above formula,
⇒

x = \frac{11 \pm \sqrt{121 - 112}}{2}

\Rightarrow x = \frac{11 \pm \sqrt{9}}{2}

\Rightarrow x = \frac{11 \pm 3}{2}

\Rightarrow x = \frac{11 - 3}{2}; x = \frac{11 + 3}{2}

⇒

x = \frac{8}{2}; x = \frac{14}{2}

\Rightarrow x = 4, 7

.
Hence, the correct option is 1.