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08 Feb 2023, 02:30
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D
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Difficulty:
35%
(medium)
Question Stats:
74% (01:54) correct
26%
(02:18)
wrong
based on 142
sessions
History
Date
Time
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Not Attempted Yet
What is the positive values of K for which quadratic equations \(x^2 + Kx + 64 = 0\) and \(x^2 – 8x + K = 0\) both will have a real roots ?
A. 10
B. 12
C. 14
D. 16
E. 18
A. 10
B. 12
C. 14
D. 16
E. 18
08 Feb 2023, 03:46
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Quadratic equation \(ax^2 + bx + c =0\) has real roots => \(b^2 - 4ac >=0\)
for quadratic equation \(x^2+ kx + 64 = 0\\
k^2 - 4*1*64 >= 0\\
k^2 >= 256\\
k^2 >=16^2\\
k >= 16\)..............1
and for quadratic equation \(x^2 – 8x + k = 0\\
64 - 4*1*k >= 0\\
64 >= 4k\\
k <= 16\) .......................2
from 1 and 2 we can deduce that k = 16
Answer D
for quadratic equation \(x^2+ kx + 64 = 0\\
k^2 - 4*1*64 >= 0\\
k^2 >= 256\\
k^2 >=16^2\\
k >= 16\)..............1
and for quadratic equation \(x^2 – 8x + k = 0\\
64 - 4*1*k >= 0\\
64 >= 4k\\
k <= 16\) .......................2
from 1 and 2 we can deduce that k = 16
Answer D
