How do you find the discriminant, describe the number and type of root, and find the exact solution using the quadratic formula given #9x^2-6x-4=-5#?

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Answer 1 · 2016-12-01T14:51:20

The solution is #S={1/3}#

Let's rewrite the quadratic equation in the form

#ax^2+bx+c=0#

#9x^2-6x-4+5=0#

#9x^2-6x+1=0#

Let's calculate the discriminant

#Delta=b^2-4ac=(-6)^2-4*9*1=36-36=0#

As, #Delta=0#, we have a double real root

#x=(-b+-sqrtDelta)/(2a)=-b/(2a)=6/18=1/3#

We can also factorise the quadratic equation

#9x^2-6x+1=(3x-1)(3x-1)=(3x-1)^2#

graph{(3x-1)^2 [-1.717, 2.128, -0.713, 1.209]}