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The roots of the equation x2+(2p-1)x+p2=0 are real if.
- a)P=1
- b)p=4
- c)p=1/4
- d)NONE
Correct answer is option 'C'. Can you explain this answer?
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The roots of the equation x2+(2p-1)x+p2=0 are real if.a)P=1b)p=4c)p=1/...
Solution:
Given equation is x2 (2p-1)x p2=0
To find: The roots of the equation are real if.
We know that for real roots of a quadratic equation, the discriminant of the equation should be non-negative.
The discriminant of the given equation is
D = (2p-1)2 - 4p2
D = 4p2 - 4p + 1 - 4p2
D = 1 - 4p + 4p2
D = (1 - 2p)2
Therefore, the discriminant is always non-negative.
Hence, the roots of the equation are real for all values of p.
Option (C) is correct.
Given equation is x2 (2p-1)x p2=0
To find: The roots of the equation are real if.
We know that for real roots of a quadratic equation, the discriminant of the equation should be non-negative.
The discriminant of the given equation is
D = (2p-1)2 - 4p2
D = 4p2 - 4p + 1 - 4p2
D = 1 - 4p + 4p2
D = (1 - 2p)2
Therefore, the discriminant is always non-negative.
Hence, the roots of the equation are real for all values of p.
Option (C) is correct.
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