Question 81418: I am suppose to decide all values of b in the following equations that will
give one or more real number solutions.
Please help me I am lost?
(a) 3x^2 + bx - 3 = 0
(b) 5x^2 + bx + 1 = 0
(c) -3x^2 + bx - 3 = 0
(d) Write a rule for judging if an equation has solutions by looking at it in standard form.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! I am suppose to decide all values of b in the following equations that will
give one or more real number solutions.
Please help me I am lost?
Here's one way:
(a) 3x^2 + bx - 3 = 0
Write two factors that will satisfy the coefficient of x^2: 3, and -3
(3x - 1)(x + 3) = 0
FOIL this and you have:
3x^2 + 9x - x - 3 = 0
3x^2 + 8x - 3 = 0; therefore b = +8
:
:
Follow the same procedure
(b) 5x^2 + bx + 1 = 0
(5x + 1)(x+1) = 0
5x^2 + 5x + 1x + 1 = 0
5x^2 + 6x + 1 = 0; b = +6
:
:
(c) -3x^2 + bx - 3 = 0
(-3x - 1) (x + 3) = 0
-3x^2 - 9x - 1x - 3 = 0
-3x^2 - 10x - 3 = 0; b = -10
:
:
(d) Write a rule for judging if an equation has solutions by looking at it in standard form.
The standard form ax^2 + bx + c = 0
Use the discriminant rules: b^2 - 4 * a * c =
Substitute for a, b, c. If the value is >0, it has real solutions
:
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