SOLUTION: find the number of solutions of 5x^2-10x-8=0 by using the discriminant. Help please, show work please and thanks.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: find the number of solutions of 5x^2-10x-8=0 by using the discriminant. Help please, show work please and thanks.       Log On


   

Question 870815: find the number of solutions of 5x^2-10x-8=0 by using the discriminant.
Help please, show work please and thanks.
Found 2 solutions by ewatrrr, richwmiller:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
discriminant is sqrt%28+b%5E2-4%2Aa%2Ac+%29
5x^2-10x-8=0
sqrt%28+100%2B160+%29+=+sqrt%28260%29
Two real solutions
y = 5(x-1)^2 -13

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Quadratic Formula
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 5%2Ax%5E2-10%2Ax-8=0 ( notice a=5, b=-10, and c=-8)





x+=+%28--10+%2B-+sqrt%28+%28-10%29%5E2-4%2A5%2A-8+%29%29%2F%282%2A5%29 Plug in a=5, b=-10, and c=-8




x+=+%2810+%2B-+sqrt%28+%28-10%29%5E2-4%2A5%2A-8+%29%29%2F%282%2A5%29 Negate -10 to get 10




x+=+%2810+%2B-+sqrt%28+100-4%2A5%2A-8+%29%29%2F%282%2A5%29 Square -10 to get 100 (note: remember when you square -10, you must square the negative as well. This is because %28-10%29%5E2=-10%2A-10=100.)




x+=+%2810+%2B-+sqrt%28+100%2B160+%29%29%2F%282%2A5%29 Multiply -4%2A-8%2A5 to get 160




x+=+%2810+%2B-+sqrt%28+260+%29%29%2F%282%2A5%29 Combine like terms in the radicand (everything under the square root)




x+=+%2810+%2B-+2%2Asqrt%2865%29%29%2F%282%2A5%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%2810+%2B-+2%2Asqrt%2865%29%29%2F10 Multiply 2 and 5 to get 10


So now the expression breaks down into two parts


x+=+%2810+%2B+2%2Asqrt%2865%29%29%2F10 or x+=+%2810+-+2%2Asqrt%2865%29%29%2F10



Now break up the fraction



x=%2B10%2F10%2B2%2Asqrt%2865%29%2F10 or x=%2B10%2F10-2%2Asqrt%2865%29%2F10



Simplify



x=1%2Bsqrt%2865%29%2F5 or x=1-sqrt%2865%29%2F5



So the solutions are:

x=1%2Bsqrt%2865%29%2F5 or x=1-sqrt%2865%29%2F5



the discriminant is 260
which tells us there are 2 real solutions