SOLUTION: What three techniques can be used to solve a quadratic equation? Demonstrate these techniques on the equation x^2-10x-39=0?

Question 199238: What three techniques can be used to solve a quadratic equation? Demonstrate these techniques on the equation x^2-10x-39=0?
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
we can use (1) factoring , (2) graphing, or (3) quadratic equation
.
(1) x^2 -10x-39 =0
(x -13) ( x+3) =0
x= +13, -3
.
check by reinserting in original,,,13^2 -130 -39 = 169 -169 =0,,,ok
(-3)^2 -10(-3) -39 = 9 =30 -39 =0,,,ok
.
(2) using graphing, create T Box
.
,,,,,,,,X,,,,,,,,,Y
,,,,,,,,,0,,,,,,,-39
,,,,,,,,-3,,,,,,,0,,,,,,,,,,x intercept
,,,,,,,,13,,,,,,,0,,,,,,,,,,x intercept
,,,,,,,,,,5,,,,,,,-64,,,,,,,vertex
.
Plot on std x / y coordinates and find x=13, -3,,,,,as zeroes
.
(3) use quadratic equation
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x = [ -(b) +/- sqrt( (b)^2 - 4 (a) (c) ) ] / 2 (a)
.
with a = (1),,,b= (-10),,,,and c= (-39)
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x = [ -(-10) +/- sqrt (-10)^2 - 4 (1) (-39) ] / 2 (1)
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x = [ 10 +/- sqrt( 100 + 156) ] /2 = 5 +/- 16/2 = +13, -3
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