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14 Aug 2023, 01:31
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A
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79% (01:32) correct
21%
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If two roots of the equation \(ax^2 + bx + c = 0\) (\(a ≠ 0\)) are reciprocals to each other and opposite in sign, what is the value of (a + c)?
A. 0
B. 1
C. 2
D. 3
E. 4
A. 0
B. 1
C. 2
D. 3
E. 4
14 Aug 2023, 02:52
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Asked: If two roots of the equation \(ax^2 + bx + c = 0\) (\(a ≠ 0\)) are reciprocals to each other and opposite in sign, what is the value of (a + c)?
Let the roots be x & -1/x
Product of roots = c/a = x*(-1/x) = - 1
c = -a
a + c = 0
IMO A
Let the roots be x & -1/x
Product of roots = c/a = x*(-1/x) = - 1
c = -a
a + c = 0
IMO A
15 Aug 2023, 03:38
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let root be m, other root is -1/m
m* -1/m = -1 = c/a
c =-a
c+a =0
m* -1/m = -1 = c/a
c =-a
c+a =0
