Question

Find the roots of quadratic equation correct to two decimal places.
$2x^2-10x+5=0$

• A. Roots are 4.44 and 0.59
• B. Roots are 4.44 and 0.56
• C. Roots are 8.44 and 0.56
• D. Roots are 4.44 and 0.90

Answer 1

The correct option is B

Roots are 4.44 and 0.56

Quadratic equation is of the form
$a{x}^2+bx+c=0$

$Wherea=2,b=–10,c=5$

Using the quadratic formula
$a{x}^2+bx+c=0,weget$

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

$=\frac{-(-10)\pm \sqrt{(-10{)}^2-(4\left)\right(2\left)\right(5)}}{2\times 2}$

$=\frac{-(-10)\pm \sqrt{100-40}}{4}$
$=\frac{-(-10)\pm \sqrt{60}}{4}$
$=\frac{10\pm 2\sqrt{15}}{4}$
$=\frac{5\pm \sqrt{15}}{2}$
$=\frac{5\pm 3.872}{2}$
$x_1=\frac{5+3.872}{2}=\frac{8.872}{2}=4.44$
$x_2=\frac{5-3.872}{2}=\frac{1.128}{2}=0.56$

Roots are 4.44 and 0.56