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If one root of the equation x2+ 7x+ p = 0 be reciprocal of the other then the value of p is________.
- a)1
- b)-1
- c)7
- d)-7
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If one root of the equation x2+ 7x+ p = 0 be reciprocal of the other t...
Given equation: x^2 + 7x + p = 0
Reciprocal roots
Let the roots of the equation be α and β such that β = 1/α
Product of roots (αβ) = 1
Using sum and product of roots formula
α + β = -7
α(1/α) = 1
α^2 = 1
α = ± 1
If α = 1, then β = 1/α = 1
If α = -1, then β = 1/α = -1
Therefore, the roots of the equation are either 1 and 1 or -1 and -1.
Value of p
Using sum and product of roots formula
α + β = -7
1 + 1 = -7 or -1 + (-1) = -7
Both equations are not satisfied.
Hence, the equation x^2 + 7x + p = 0 cannot have reciprocal roots.
Therefore, the answer is option A) 1.
Reciprocal roots
Let the roots of the equation be α and β such that β = 1/α
Product of roots (αβ) = 1
Using sum and product of roots formula
α + β = -7
α(1/α) = 1
α^2 = 1
α = ± 1
If α = 1, then β = 1/α = 1
If α = -1, then β = 1/α = -1
Therefore, the roots of the equation are either 1 and 1 or -1 and -1.
Value of p
Using sum and product of roots formula
α + β = -7
1 + 1 = -7 or -1 + (-1) = -7
Both equations are not satisfied.
Hence, the equation x^2 + 7x + p = 0 cannot have reciprocal roots.
Therefore, the answer is option A) 1.
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Community Answer
If one root of the equation x2+ 7x+ p = 0 be reciprocal of the other t...
Product of roots of a quadratic equation ax^2 + bx + c = 0
Is c
Here product of roots = x * 1/x = 1
Therefore p = 1
Is c
Here product of roots = x * 1/x = 1
Therefore p = 1
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