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Question 819271: [ Write the quadratic equation whose roots are 2 and -5 , and whose "a" coefficient in the standard form is 2 ]
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! ---
f(x) = ax^2 + bx + c
f(x) = 2x^2 + bx + c
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roots are 2 and -5:
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0 = 2(2)^2 + b(2) + c
0 = 8 + 2b + c
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0 = 2(-5)^2 + b(-5) + c
0 = 50 - 5b + c
c = 5b - 50
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8 + 2b + c = 0
8 + 2b + 5b - 50 = 0
7b = 42
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b = 6
c = -20
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answer:
f(x) = 2x^2 + 6x - 20
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check:
the above quadratic equation is in standard form, with a=2, b=6, and c=-20
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to solve the quadratic equation by using the quadratic formula, plug this:
2 6 -20
into this: https://sooeet.com/math/quadratic-equation-solver.php
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the two real roots of the quadratic are:
x = 2
x = -5
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exactly the given roots, so the result is correct
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