SOLUTION: Find an integer c such that the equation 4x^2+cx=9=0 has a double real root. please help me with this problem thank you.

Question 939556: Find an integer c such that the equation 4x^2+cx=9=0 has a double real root.
please help me with this problem thank you.
Found 4 solutions by stanbon, josgarithmetic, MathLover1, MathTherapy:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Find an integer c such that the equation 4x^2+cx+9=0 has a double real root.
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Condition required to have double real root:: b^2-4ac = 0
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Solve:: c^2 -4*4*9 = 0
c^2 -144 = 0
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(c-12)(c+12) = 0
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c = 12 or c = -12
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Cheers,
Stan H.
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Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Want two solutions.
You wrote two equality symbols, so I am using the first of them as a PLUS sign.

Try discriminant. You do not want a square, but you want two different solutions for x.

The discriminant needs to be positive.

------------the value if exactly one real root. But you want TWO real roots, and want c as integer.

c can be any of c=13 or c=14, or ANY integer greater than 12.
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

A double root occurs when the quadratic is a perfect square trinomial.
4x^2+cx=9=0 I guess you have
use a rule a perfect square
note that , , and
=> ; so, the integer is
so, a perfect square trinomial is

or and solution is a double root
=> => each factor is and it is equal to zero if =>

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Find an integer c such that the equation 4x^2+cx=9=0 has a double real root.
please help me with this problem thank you.

----- Assuming that the extra �=� sign is actually �+�
Let c be p to prevent confusion, so the equation now becomes:
For this equation to have a double real root, its discriminant: will equal 0 (zero)
Therefore, with a being 4; b being p; and c being 9, we get:

, or p, or
Therefore, in , c will have a value of in order for the equation to have a double root solution.
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