SOLUTION: For 5x^2+3x-2 do the following -graphing (both in vertex form and in standard form) -factoring/pp -completing the square/square roots -quadratic formula.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: For 5x^2+3x-2 do the following -graphing (both in vertex form and in standard form) -factoring/pp -completing the square/square roots -quadratic formula.      Log On


   

Question 141122: For 5x^2+3x-2 do the following

-graphing (both in vertex form and in standard form)
-factoring/pp
-completing the square/square roots
-quadratic formula.
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
5x^2+3x-2=0
.
factoring:
5*-2=-10
What 2 factors of -10 add up 3? Ans: 5 and -2.
5x^2+5x-2x-2=0
5x(x+1)-2(x+1)=0 Factoring by grouping.
(5x-2)(x+1)=0
5x=2 x=2/5
x=-1
.
Completing the square:
5x^2+3x-2=0
x^2+ 3x/5 - 2/5 = 0
x^2+.6x-.4=0
x^2+.6x =.4
x^2+.6x+.09=.4+.09 Complete the square by dividing the middle term by 2 and squaring the result.
(x+.3)^2=.49
x+.3=+-.7
x=-.3+-.7
x=.4, x=-1
.
Ed
.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B3x%2B-2+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%283%29%5E2-4%2A5%2A-2=49.

Discriminant d=49 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+49+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+49+%29%29%2F2%5C5+=+0.4
x%5B2%5D+=+%28-%283%29-sqrt%28+49+%29%29%2F2%5C5+=+-1

Quadratic expression 5x%5E2%2B3x%2B-2 can be factored:
5x%5E2%2B3x%2B-2+=+%28x-0.4%29%2A%28x--1%29
Again, the answer is: 0.4, -1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B3%2Ax%2B-2+%29