Question

If the square of a number is 80 less than 18 times the number, then the number can be .

• A. 8 or 10
• B. -8 or -10
• C. -8 or 10
• D. 8 or -10

Answer 1

The correct option is A 8 or 10

Let the number be $x$.
Square of the number = $x^2$
Given, the square of the number is 80 less than 18 times the number
$\Rightarrow$ $x^2$ = $18x$ -80
$\Rightarrow$ $x^2$ - $18x$ +80 = 0

The roots of a quadratic equation $a{x}^2+bx+c=0$ is given by $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$.

Hence, the roots are $x=\frac{18\pm \sqrt{(-18{)}^2-4\times 1\times 80}}{2\times 1}$

$x=\frac{18\pm \sqrt{324-(4\times 80)}}{2}$

$x=\frac{18\pm \sqrt{4}}{2}$

$x=\frac{18\pm 2}{2}$

$x=8or10$