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# For integers a and x, which of the following values of a guarantees

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Re: For integers a and x, which of the following values of a guarantees [#permalink]
I did not get the fundamental of this question. So becasue the two roots of the first answer choice are 2 and 2, it is a perfect square? - please correct me if I am wrong. thank you.
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Re: For integers a and x, which of the following values of a guarantees [#permalink]
Bunuel wrote:
For integers $$a$$ and $$x$$, which of the following values of $$a$$ guarantees that $$4x^2 + ax + 16$$ is a perfect square?

A. −16
B. −4
C. 4
D. 8
E. 12

Now, $$4x^2 + ax + 16$$ can be of the forms $$(2x)^2 - 2(2x)(4) + (4)^2$$ = $$4x^2 - 16x + 16$$

Hence, we have -16x = ax

Thus, a = -16

Thus, correct answer will be (A) -16
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Re: For integers a and x, which of the following values of a guarantees [#permalink]
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For any quadratic equation ax^2+bx+c = 0 roots are given by
[-b+Root(b^2-4ac)]/2a and [-b-Root(b^2-4ac)]/2a
For roots to be equal b^2-4ac = 0
Applying it here
a=16,-16
From options we get -16 as the answer.
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For integers a and x, which of the following values of a guarantees [#permalink]
OreoShake wrote:
I did not get the fundamental of this question. So becasue the two roots of the first answer choice are 2 and 2, it is a perfect square? - please correct me if I am wrong. thank you.

2 is the root of the equation.Question is whether the equations boils down to a perfect square.
If you put values of x and a in the equation it will result in to zero.Zero is a perfect square.
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Re: For integers a and x, which of the following values of a guarantees [#permalink]
For any quadratic equation ax^2+bx+c = 0 roots
For roots to be equal D, b^2-4ac = 0, distinct if D >0, No roots if D<0
Applying it here
a=16,-16
Checking options, -16 is the answer.
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Re: For integers a and x, which of the following values of a guarantees [#permalink]
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Re: For integers a and x, which of the following values of a guarantees [#permalink]
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