Question 194179: Determine the number of solutions and classify the type of solutions for each of the following equations. Justify your answer.
4x2 + 16x + 16 = 0
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! 4x^2 + 16x +16 =0
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4 (x^2 + 4x + 4) =0
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check Discriminant, remember, D less than 0, no solutions
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,D =0,,,,,one solution
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,D > 0,,,,,two solutions
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a=1,,b=4,,,c=4,,,,and D = sqrt ( b^2 - 4 * a * c ) = sqrt ( 16 -4 * 1 * 4 ) =0
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therefore one solution
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factoring ( x^2 +4x +4 ) = (x+2) (x+2 ),,, x=-2,,and -2,,
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this is a duplicate solution and counts as 1 (one) solution
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The function is a positive parabola, cup pointed up, with vertex just touching y axis, at x=-2
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