Question

Find all values of $m$ for which the quadratic equation $2x^2+3x-m+2=0$ have two distinct real solutions.

• A. $m>\frac{25}{8}$
• B. $m>\frac{4}{8}$
• C. $m>\frac{3}{8}$
• D. None of these

Answer 1

The correct option is A $m>\frac{25}{8}$

Condition for the quadratic equation to have distinct roots

$Discriminant=b^2-4ac>0$

Given equation, $2x^2+3x-m+2=0$

$a=2,b=3,c=-m+2$

$Discriminant=3^2-4\left(2\right)(-m+2)>0$

$9-8(m-2)>0$

$9-8m+16>0$

$8m>25$

$m>\frac{25}{8}$