Question

Find the value of $k$ for which the equation, ${2x}^2+3x+k=0$ distinct real roots.

Answer 1

Given :The roots are real and distinct

$\Rightarrow$ Discriminant$\Delta =b^2-4ac>0$

where $a=2,b=3,c=k$

$\Delta =3^2-4\times 2\times k>0$

$\Rightarrow 9-8k>0$

$\Rightarrow -8k>-9$

$\Rightarrow 8k<9$

$\Rightarrow k<\frac{9}{8}$

$\therefore k\in (-\infty ,\frac{9}{8})$