Question 154636This question is from textbook elementary and intermediate algebra concepts and applications
: I really need help can somebody polease help me?
1. Determine whether the following equations have a solution or not? Justify your answer.
a) x2 + 6x - 7 = 0
b) z2 + z + 1 = 0
c) (3)1/2y2 - 4y - 7(3)1/2 = 0
d) 2x2 - 10x + 25 = 0
e) 2x2 - 6x + 5 = 0
f) s2 - 4s + 4 = 0
g) 5/6x2 - 7x - 6/5 = 0
h) 7a2 + 8a + 2 = 0
2. If x = 1 and x = -8, then form a quadratic equation.
3. What type of solution do you get for quadratic equations where D < 0? Give reasons for your answer. Also provide an example of such a quadratic equation and find the solution of the equation.
4. Create a real-life situation that fits into the equation (x + 4)(x - 7) = 0 and express the situation as the same equation.
This question is from textbook elementary and intermediate algebra concepts and applications
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1. Determine whether the following equations have a solution or not? Justify your answer.
a) x2 + 6x - 7 = 0
b) z2 + z + 1 = 0
c) (3)1/2y2 - 4y - 7(3)1/2 = 0
d) 2x2 - 10x + 25 = 0
e) 2x2 - 6x + 5 = 0
f) s2 - 4s + 4 = 0
g) 5/6x2 - 7x - 6/5 = 0
h) 7a2 + 8a + 2 = 0
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Comment: You have a bunch of quadratic equations.
I assume you know what a,b, and c are for a quadratic:
e.g. for your "d" problem (above), a= 2, b = 10, c = 25
I assume you know that D (below) is the discriminant
and that D = b^2 - 4ac for any quadratic
You may not know the following:
When D>0, the quadratic has two unequal Real Number solutions.
When D=0, the quadratic has two equal Real Number solutions.
when D<0, the quadratic has two different Complex Number solutions
e.g. for "d" (above) D = 10^2-4*2*25 = 0
So "d" has two equal Real Number solutions.
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2. If x = 1 and x = -8, then form a quadratic equation.
f(x) = (x-1)(x+8)
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3. What type of solution do you get for quadratic equations where D < 0? Give reasons for your answer. Also provide an example of such a quadratic equation and find the solution of the equation.
Ans: You have a quadratic with two Complex Number solutions.
Ex: f(x) = 2x^2 -3x + 20 where D= 9-4*2*20 = -151 < 0
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4. Create a real-life situation that fits into the equation (x + 4)(x - 7) = 0 and express the situation as the same equation.
Ex: My family finances were zero 4 years ago and by looking at the economy
I expect they will be zero again 7 years from now. Graph a function that
tracks my finances if I am $28 in debt at the present time.
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Cheers,
Stan H.
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