Question 242975: Given that one of the roots of the quadratic equation 4x^2-(p-2)x-2p=5 is negative of the other root,find
(a)the value of p,
(b)the roots of the quadratic equation
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Given that one of the roots of the quadratic equation 4x^2-(p-2)x-2p=5 is negative of the other root,find
(a)the value of p,
Let x and -x be the roots.
Then,
4x^2-(p-2)x-2p-5 = 0
And, replacing x with -x,
4x^2 + (p-2)x -2p -5 = 0
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Subtracting the 1st from the 2nd you get:
2(p-2)x = 0
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So x = 0 or p = 2
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(b)the roots of the quadratic equation
4x^2-(p-2)x-2p=5
If p =2
4x^2 -2p = 5
4x^2= 2p+5
x^2 = (2p+5)/4
x = +-sqrt[(2p+5)/4]
Since p = 2
x = +-sqrt[9/4]
x = +-3/2
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Cheers,
Stan H.
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