Question

If the roots of the equation $x^2-8x+a^2-60=0$ are real, then the value of $a$ is

• A. $-2\ge a\ge 8$
• B. $-2<a<8$
• C. $-2>a>8$
• D. $2<a<8$

Answer 1

Answer: (A)

$\because$ Roots of the equation
$x^2-8x+a^2-6a=0$ are real.
$\therefore$ $B^2-4AC\ge 0$
$\Rightarrow$ ${(8)}^2-4(1)(a^2-6a)\ge 0$
$\Rightarrow$ $64-4a^2+24a\ge 0$
$\Rightarrow$ $16-a^2+6a\ge 0$
$\Rightarrow$ $a^2-6a-16\le 0$
$\Rightarrow$ $(a+2)(a-8)\le 0$
$\Rightarrow$ $-2\le a\le 8$