Question

The set of values of k for which the given quadratic equation has real roots
$3x^2$ + 2x + k = 0 is k $\le \frac{1}{3}$

• A. True
• B. False

Answer 1

The correct option is A True

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

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

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

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

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

$\Rightarrow$ $4-12k\ge$

$\Rightarrow$ $-12k\ge -4$

$\Rightarrow$ $3k\le 1$

$\therefore$ $k\le \frac{1}{3}$

$\therefore$ We can see that value $k$ given question are correct.