Question 182117
18) -12x^2 + 5x + 2 = 0
:
a) find the value of the discriminant
discrim = b^2 - 4*a*c
In this equation: a=-12; b=5; c=2, so we have
d = 5^2 + 4 * -12 * 2
d = 25 - (-96)
d = 25 + 96
d = +121
:
b) describe the number and type of roots
d > 0 therefore,  two different real roots
:
c) find the exact solutions by using the Quadratic Formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
we already found the value of the discriminant, so we can write it
{{{x = (-5 +- sqrt(121))/(2*-12) }}} 
Two solutions:
{{{x = (-5 + 11)/(-24) }}}
{{{x = 6/(-24)}}}
{{{x = -1/4}}}
and
{{{x = (-5 - 11)/(-24) }}}
{{{x =(-16)/(-24)}}}
{{{x = 2/3}}}