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.

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) (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 (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=49 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 0.4, -1. Here's your graph:

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