SOLUTION: one of the roots of the equation 5x^2 + kx = 4 is x = -2 the other root is x = ...what ? a -5/2 b -2/5 c 2/5 d 2 e 5/2

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: one of the roots of the equation 5x^2 + kx = 4 is x = -2 the other root is x = ...what ? a -5/2 b -2/5 c 2/5 d 2 e 5/2       Log On


   

Question 252441: one of the roots of the equation 5x^2 + kx = 4 is x = -2 the other root is
x = ...what ?
a -5/2 b -2/5 c 2/5 d 2 e 5/2
Found 2 solutions by richwmiller, stanbon:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
plug -2 in for x and solve for k
then solve the equation
5(-2)^2+k(-2)=4
5*4-2k=4
subtract 4 from each side
4*4-2k=0
add 2k to each side
16=2k
8=k
5x^2+8x=4
5x^2+8x-4=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B8x%2B-4+=+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=%288%29%5E2-4%2A5%2A-4=144.

Discriminant d=144 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-8%2B-sqrt%28+144+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%288%29%2Bsqrt%28+144+%29%29%2F2%5C5+=+0.4
x%5B2%5D+=+%28-%288%29-sqrt%28+144+%29%29%2F2%5C5+=+-2

Quadratic expression 5x%5E2%2B8x%2B-4 can be factored:
5x%5E2%2B8x%2B-4+=+5%28x-0.4%29%2A%28x--2%29
Again, the answer is: 0.4, -2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B8%2Ax%2B-4+%29

.4=2/5
you could also have divided x+2 into the equation

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
one of the roots of the equation 5x^2 + kx = 4 is x = -2 the other root is
x = ...what ?
--------------------------
f(-2) = 0
5(-2)^2+k(-2)= 4
20-2k=4
2k = 16
k = 8
----------------
5x^2+8x-4 = 0
5x^2+10x-2x-4 = 0
5x(x+2)-2(x+2) = 0
(x-2)(5x-2) = 0
x = 2 or x = 2/5
------------------------
Ans: x = 2/5
============================
Cheers,
Stan H.

a -5/2 b -2/5 c 2/5 d 2 e 5/2