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An object is launched from a platform. Its height (in meters), xxx seconds after the launch, is modeled by: h(x)=-5x^2+20x+60h(x)=−5x 2 +20x+60h, left parenthesis, x, right parenthesis, equals, minus, 5, x, start superscript, 2, end superscript, plus, 20, x, plus, 60 How many seconds after launch will the object land on the ground?

Respuesta :

It takes 6 seconds for it to hit the ground.

0 = -5x²+20x+60

We can solve this by factoring.  First factor out the GCF, -5:

0 = -5(x²-4x-12)

Now we want factors of -12 that sum to -4.  -6(2) = -12 an -6+2 = -4:
0 = -5(x-6)(x+2)

Using the zero product property, we know that either x-6=0 or x+2=0; this gives us the answers x=6 or x=-2.  Since we cannot have negative time, x=6.

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