Question

Which of the following is/are the roots of the quadratic equation,
$x^2-7x+10=0$ ?

• A. $x=-2$
• B. $x=-5$
• C. $x=5$
• D. $x=2$

Answer 1

Answer: (C), (D)

$x=2$

Given,
$x^2-7x+10=0$
Using completing the square method we can write,
$x^2-2\left(x\right)\left(\frac{7}{2}\right)+(\frac{7}{2}{)}^2+10-(\frac{7}{2}{)}^2$
$\Rightarrow (x-\frac{7}{2}{)}^2+10-(\frac{7}{2}{)}^2=0$
$\Rightarrow (x-\frac{7}{2}{)}^2=-10+\frac{49}{4}$
$\Rightarrow (x-\frac{7}{2}{)}^2=\frac{-40}{4}+\frac{49}{4}$
$\Rightarrow (x-\frac{7}{2}{)}^2=\frac{9}{4}$
$\Rightarrow (x-\frac{7}{2})=\pm \frac{3}{2}$
$\Rightarrow x=2$ or $x=5$