Question

The set of values of k for which the given quadratic equation has real roots
2$x^2$ + kx + 2 = 0 is k $\le$ -4 or k $\ge$ 4

• A. True
• B. False

Answer 1

The correct option is A True

$\Rightarrow$ The given quadratic equation is $2x^2+kx+2=0$, comparing it with $a{x}^2+bx+c=0$

$\Rightarrow$ We get, $a=2,b=k,c=2$

$\Rightarrow$ It is given that roots are real

$\therefore$ $b^2-4ac\ge 0$

$\Rightarrow$ $(k{)}^2-4(2\left)\right(2)\ge 0$

$\Rightarrow$ $k^2-16\ge 0$

$\Rightarrow$ $(k{)}^2-(4{)}^2\ge 0$

$\Rightarrow$ $(k+4)(k-4)\ge 0$

$\therefore$ $k\le -4$ or $k\ge 4$

$\Rightarrow$ Given value of $k$ in question are correct.