Question 678154: How do you write a quadratic equation in the form ax^2 + bx + c = 0 such that c = 4 and the equation has the given solutions of -4 and 3? Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website! How do you write a quadratic equation in the form ax^2 + bx + c = 0 such that c = 4 and the equation has the given solutions of -4 and 3?
because you are given that c=4 we have two equations and two unknowns:
since x= -4 is a solution:
a(-4)^2 + b(-4) + 4 = 0
16a - 4b + 4 = 0 (equation 1)
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since x= 3 is a solution:
a(3)^2 + b(3) + 4 = 0
9a + 3b + 4 = 0 (equation 2)
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System of equation:
16a - 4b + 4 = 0
9a + 3b + 4 = 0
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multiply top by 3 and bottom by 4:
48a - 12b + 12 = 0
36a + 12b + 16 = 0
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84a + 28 = 0
84a = -28
a = -28/84
a = -1/3
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plug above into:
9a + 3b + 4 = 0
9(-1/3) + 3b + 4 = 0
-3 + 3b + 4 = 0
3b + 1 = 0
3b = -1
b = -1/3
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our final answer:
(-1/3)x^2 - (1/3)x + 4 = 0
