SOLUTION: i need to use the discriminant to determine the number of solutions of this quadratic equation, and whether the solutions are real or complex. i have to find the roots, but i do h

Algebra ->  Graphs -> SOLUTION: i need to use the discriminant to determine the number of solutions of this quadratic equation, and whether the solutions are real or complex. i have to find the roots, but i do h      Log On


   

Question 144574: i need to use the discriminant to determine the number of solutions of this quadratic equation, and whether the solutions are real or complex. i have to find the roots, but i do have to determine the number and types of solutions. x2 + 6x - 7 = 0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

D=b%5E2-4ac Start with the discriminant formula

D=%286%29%5E2-4%2A1%2A-7 Plug in a=1, b=6, c=-7

D=36-4%2A1%2A-7 Square 6 to get 36

D=36%2B28 Multiply -4*1*-7 to get 28

D=64 Combine 36 and 28 to get 64


Since the discriminant equals 64 (which is greater than zero) , this means there are two real solutions.



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%2B6%2Ax-7=0 ( notice a=1, b=6, and c=-7)




x+=+%28-6+%2B-+sqrt%28+%286%29%5E2-4%2A1%2A-7+%29%29%2F%282%2A1%29 Plug in a=1, b=6, and c=-7



x+=+%28-6+%2B-+sqrt%28+36-4%2A1%2A-7+%29%29%2F%282%2A1%29 Square 6 to get 36



x+=+%28-6+%2B-+sqrt%28+36%2B28+%29%29%2F%282%2A1%29 Multiply -4%2A-7%2A1 to get 28



x+=+%28-6+%2B-+sqrt%28+64+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-6+%2B-+8%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%28-6+%2B-+8%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%28-6+%2B+8%29%2F2 or x+=+%28-6+-+8%29%2F2

Lets look at the first part:

x=%28-6+%2B+8%29%2F2

x=2%2F2 Add the terms in the numerator
x=1 Divide

So one answer is
x=1



Now lets look at the second part:

x=%28-6+-+8%29%2F2

x=-14%2F2 Subtract the terms in the numerator
x=-7 Divide

So another answer is
x=-7

So our solutions are:
x=1 or x=-7