Question

Solve the quadratic equationn $x^2-5x-10=0$ correct to 2 decimal places.

• A. Roots are 6.93 and -1.53
• B. Roots are 6.53 and -1.53
• C. Roots are 6.53 and -1.59
• D. Roots are 6.53 and -6.53

Answer 1

The correct option is B

Roots are 6.53 and -1.53

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

$Wherea=1,b=–5,c=-10$

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

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

$=\frac{-(-5)\pm \sqrt{(5{)}^2-(4\left)\right(1\left)\right(-10)}}{2\times 1}$

$=\frac{5\pm \sqrt{25+40}}{2}$
$=\frac{5\pm \sqrt{65}}{2}$
$=\frac{5\pm 8.062}{2}$
$x_1=\frac{5+8.062}{2}=\frac{13.062}{2}=6.531$
$x_2=\frac{5-8.062}{2}=\frac{-3.062}{2}=-1.531$

Roots are 6.53 and -1.53