How do you find the discriminant, describe the number and type of root, and find the exact solution using the quadratic formula given #-3x^2-5x+2=0#?

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Answer 1 · 2016-11-23T13:39:39

The solution is # S={-2,1/3} #

The equation is #-3x^2-5x+2=0#

The quadratic equation is #ax^2+bx+c=0#

We start by calculating the discriminant

#Delta = b^2-4ac=(-5)^2-4(-3)(+2)#
#=25+27=49#

As, #Delta >0#, we expect 2 real roots

The roots are
#=(-b+-sqrtDelta)/(2a)#

#x_1=(5+7)/(-6)=-2#

#x_2=(5-7)/(-6)=1/3#