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If c is a constant and x is a variable, what is the value of c in the

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Bunuel
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If c is a constant and x is a variable, what is the value of c in the [#permalink] New post   06 Jan 2021, 06:37
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If c is a constant and x is a variable, what is the value of c in the equation \(x^2 + 24x + c = 0\)?

(1) The equation \(x^2 + 24x + c = 0\) has exactly one distinct solution.
(2) c is less than or equal to 144
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If c is a constant and x is a variable, what is the value of c in the [#permalink] New post   06 Jan 2021, 07:56
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Bunuel wrote:
If c is a constant and x is a variable, what is the value of c in the equation \(x^2 + 24x + c = 0\)?

(1) The equation \(x^2 + 24x + c = 0\) has exactly one distinct solution.
(2) c is less than or equal to 144



If the quadratic equation is \(ax^2+bx+c=0\),
Sum of roots = \(\frac{-b}{a}\)
Product of roots = \(\frac{c}{a}\)

\(x^2 + 24x + c = 0\) is the quadratic equation here.
Sum of roots = \(\frac{-b}{a}=-24\)
Product of roots = \(\frac{c}{a}=c\)

(1) The equation \(x^2 + 24x + c = 0\) has exactly one distinct solution.
So Sum = \(x+x=2x=-24....x=-12\). Thus \(c=x*x=(-12)^2=144\).
OR
\(x^2 + 24x + c = 0\) having exactly one distinct solution means it is of the form \(a^2+2ab+b^2=0\).
Thus \(x^2 + 24x + c = 0........x^2+2*12*x+c=0.....x^2+2*12*x+12^2=0.....c=12^2=144\)
Sufficient
(2) c is less than or equal to 144
Clearly insufficient.

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Re: If c is a constant and x is a variable, what is the value of c in the [#permalink] New post   06 Jan 2021, 10:29
Bunuel wrote:
If c is a constant and x is a variable, what is the value of c in the equation \(x^2 + 24x + c = 0\)?

(1) The equation \(x^2 + 24x + c = 0\) has exactly one distinct solution.
(2) c is less than or equal to 144


(1) Quadratic equation has exactly one distinct solution when D = 0
D = \(b^2 - 4ac\) = 0
\(b^2 \)= 4ac
c = \(b^2/4a\) = \(24^{2}/4\) = 144
Sufficient

(2) c can be any value less than or equal to 144
Insufficient

A is correct
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If c is a constant and x is a variable, what is the value of c in the [#permalink] New post   26 Jan 2021, 02:06
Answer A
at the time of one distinct root the delta =0 i.e b^2 -4ac=0
24*24-4c=0
-4c=-576
c=144
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If c is a constant and x is a variable, what is the value of c in the [#permalink]
26 Jan 2021, 02:06
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