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The equation x2 –(p+4)x + 2p + 5 = 0 has equal roots the values of p will be.
- a)± 1
- b)2
- c)± 2
- d)–2
Correct answer is option 'C'. Can you explain this answer?
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The equation x2 (p+4)x + 2p + 5 = 0 has equal roots the values of p wi...
Given equation: x^2 + (4p)x + 2p + 5 = 0
For equal roots, the discriminant (b^2 - 4ac) of the quadratic equation must be equal to zero.
So, we have:
(4p)^2 - 4(1)(2p + 5) = 0
16p^2 - 8p - 20 = 0
Dividing throughout by 4, we get:
4p^2 - 2p - 5 = 0
Using the quadratic formula, we get:
p = [2 ± √(4 + 80)]/8
p = [2 ± √84]/8
p = [1 ± √21]/4
Since we are given that the roots are equal, we must have only one value of p, so we take the positive value of the square root:
p = (1 + √21)/4
Therefore, the correct answer is option C.
For equal roots, the discriminant (b^2 - 4ac) of the quadratic equation must be equal to zero.
So, we have:
(4p)^2 - 4(1)(2p + 5) = 0
16p^2 - 8p - 20 = 0
Dividing throughout by 4, we get:
4p^2 - 2p - 5 = 0
Using the quadratic formula, we get:
p = [2 ± √(4 + 80)]/8
p = [2 ± √84]/8
p = [1 ± √21]/4
Since we are given that the roots are equal, we must have only one value of p, so we take the positive value of the square root:
p = (1 + √21)/4
Therefore, the correct answer is option C.
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The equation x2 (p+4)x + 2p + 5 = 0 has equal roots the values of p will be.a) 1b)2c) 2d)2Correct answer is option 'C'. Can you explain this answer?
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