Question 823037: 5x^2-6x-h=0
Please help!
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! first look at the discriminant of this quadratic equation
5x^2-6x-h=0, which is
b^2 - 4*a*c, now substitute what we know
(-6)^2 - 4*5*(-h)
36+20*h
now is there a value of h that gives us a rational square root?
if h = 8, then we have
square root of (36+20*8) is 14 and using quadratic formula
x = (-(-6) + 14) / (2*5) = 2
x = (-(-6) - 14) / (2*5) = -4/5
now we have
5x^2 -6x -8 = 0
if x = 2, then
5*2^2 -6*2 -8 = 0
20 -12 -8 = 0
0 = 0
x = 2 checks
now try -4/5
5*(-4/5)^2 -6*(-4/5) -8 = 0
16/5 + 24/5 -8 = 0
40/5 -8 = 0
8 -8 = 0
answer checks
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