Question

The set of values of k for which the given below quadratic equation has the real roots is k $\le 4\sqrt{6}$.

$2x^2+kx+3=0$ .

• A. True
• B. False

Answer 1

The correct option is B False

$\Rightarrow$ The given quadratic equation is $2x^2+kx+3=0$, comparing it with $a{x}^2+bx+c=0$

$\Rightarrow$ We get, $a=2,b=k,c=3$

$\Rightarrow$ It is given that roots are real.

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

$\Rightarrow$ $(k{)}^2-4(2\left)\right(3)\ge 0$

$\Rightarrow$ $k^2-24\ge 0$

$\Rightarrow$ $(k{)}^2-(2\sqrt{6}{)}^2\ge 0$

$\Rightarrow$ $(k+2\sqrt{6})(k-2\sqrt{6})\ge 0$

$\Rightarrow$ $k\ge 2\sqrt{6}$ or $k\le -2\sqrt{6}$

$\therefore$ We can see the value of $k$ given in the question is incorrect.