SOLUTION: find the x-intercepts y=x^2+5x+2

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Question 102538: find the x-intercepts
y=x^2+5x+2
Answer by jim_thompson5910(28715) About Me  (Show Source):
You can put this solution on YOUR website!
To find the x-intercepts, let y=0 and solve for x

0=x%5E2%2B5x%2B2

Let's use the quadratic formula to solve for x:


Starting with the general quadratic

ax%5E2%2Bbx%2Bc=0

the general solution using the quadratic equation is:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29



So lets solve x%5E2%2B5%2Ax%2B2=0 ( notice a=1, b=5, and c=2)




x+=+%28-5+%2B-+sqrt%28+%285%29%5E2-4%2A1%2A2+%29%29%2F%282%2A1%29 Plug in a=1, b=5, and c=2



x+=+%28-5+%2B-+sqrt%28+25-4%2A1%2A2+%29%29%2F%282%2A1%29 Square 5 to get 25



x+=+%28-5+%2B-+sqrt%28+25%2B-8+%29%29%2F%282%2A1%29 Multiply -4%2A2%2A1 to get -8



x+=+%28-5+%2B-+sqrt%28+17+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-5+%2B-+sqrt%2817%29%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%28-5+%2B+sqrt%2817%29%29%2F2 or x+=+%28-5+-+sqrt%2817%29%29%2F2


Now break up the fraction


x=-5%2F2%2Bsqrt%2817%29%2F2 or x=-5%2F2-sqrt%2817%29%2F2



So these expressions approximate to

x=-0.43844718719117 or x=-4.56155281280883


So our solutions are:
x=-0.43844718719117 or x=-4.56155281280883

Notice when we graph x%5E2%2B5%2Ax%2B2, we get:



when we use the root finder feature on a calculator, we find that x=-0.43844718719117 and x=-4.56155281280883.So this verifies our answer