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Math Algebra question If one of the roots of the quadratic equation dx to the 2 plus 5x minus 3 equals 0 is x equals -3 A Determine the value of d and B Determine the other root Please help?
Tanner199
Answers:
A) d = 2
B) x = 1/2
Why?
We have dx2 + 5x - 3 = 0, and one solution is x = -3.
The equation is quadratic, so it can be factored into two linear terms (things that look like ax+b). Since,
x = -3
x + 3 = -3 +3
x + 3 = 0
So x + 3 is one of the terms.
So dx2 + 5x - 3 = 0 is equivalent to
(?x + ?)(x + 3) = 0
The first ? must be d since ?x*x = dx2. The second ? must be -1 since ?*3 = -3.
So we have
(dx - 1)(x + 3) = 0
When we distribute (students often know as F.O.I.L.), we find that
dx2+ 3dx - x - 3 = 0
dx2+ (3d-1)x - 3 = 0 (factor out x, or think of combining like terms) This is the same as:
dx2 + 5x - 3 = 0 So we know 3d - 1 = 5, an equation we can solve for d.
3d - 1 = 5
3d - 1 + 1 = 5 + 1
3d = 6
3d/3 = 6/3
d = 2
Yay! Part A of your problem is complete: d = 2.
Next, Part B, we must find the other root, or solution.
So now we have
2x2 + 5x - 3 = 0 is the same as
(2x - 1)(x + 3) = 0 so we know
2x - 1 = 0
2x - 1 + 1 = 0 + 1
2x = 1
2x/2 = 1/2
x = 1/2
So for Part B, we have x = 1/2 is the other root.
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