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06 Jan 2021, 06:37
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
65% (01:24) correct
35%
(01:50)
wrong
based on 115
sessions
History
Date
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Not Attempted Yet
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) The equation \(x^2 + 24x + c = 0\) has exactly one distinct solution.
(2) c is less than or equal to 144
06 Jan 2021, 07:56
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Bunuel
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.
A
06 Jan 2021, 10:29
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Bunuel
(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
