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If alpha and beta are the zeroes of polynomial P(x)=x^2+x-1 then 1/alpha+1/beeta
a. 1
b.2
c. -1
d.-1/2?
a. 1
b.2
c. -1
d.-1/2?
Most Upvoted Answer
If alpha and beta are the zeroes of polynomial P(x)=x^2+x-1 then 1/alp...
Explanation:
Given:
P(x) = x^2 + x - 1
Let alpha and beta be the zeroes of the polynomial P(x)
Finding 1/alpha + 1/beta:
1. We know that the sum of the roots of a quadratic equation ax^2 + bx + c = 0 is given by -b/a. Therefore, the sum of the roots alpha and beta is -1.
2. We need to find 1/alpha + 1/beta, which is equivalent to (alpha + beta)/(alpha * beta) using the formula for the product of roots of a quadratic equation.
3. From step 1, we know that alpha + beta = -1 and from the given polynomial, we have alpha * beta = -1.
4. Therefore, 1/alpha + 1/beta = (-1)/(-1) = 1.
Conclusion:
Hence, 1/alpha + 1/beta = 1.
Therefore, the correct answer is:
c. 1
Given:
P(x) = x^2 + x - 1
Let alpha and beta be the zeroes of the polynomial P(x)
Finding 1/alpha + 1/beta:
1. We know that the sum of the roots of a quadratic equation ax^2 + bx + c = 0 is given by -b/a. Therefore, the sum of the roots alpha and beta is -1.
2. We need to find 1/alpha + 1/beta, which is equivalent to (alpha + beta)/(alpha * beta) using the formula for the product of roots of a quadratic equation.
3. From step 1, we know that alpha + beta = -1 and from the given polynomial, we have alpha * beta = -1.
4. Therefore, 1/alpha + 1/beta = (-1)/(-1) = 1.
Conclusion:
Hence, 1/alpha + 1/beta = 1.
Therefore, the correct answer is:
c. 1
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If alpha and beta are the zeroes of polynomial P(x)=x^2+x-1 then 1/alpha+1/beetaa. 1 b.2c. -1d.-1/2? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If alpha and beta are the zeroes of polynomial P(x)=x^2+x-1 then 1/alpha+1/beetaa. 1 b.2c. -1d.-1/2? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alpha and beta are the zeroes of polynomial P(x)=x^2+x-1 then 1/alpha+1/beetaa. 1 b.2c. -1d.-1/2?.
If alpha and beta are the zeroes of polynomial P(x)=x^2+x-1 then 1/alpha+1/beetaa. 1 b.2c. -1d.-1/2? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If alpha and beta are the zeroes of polynomial P(x)=x^2+x-1 then 1/alpha+1/beetaa. 1 b.2c. -1d.-1/2? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If alpha and beta are the zeroes of polynomial P(x)=x^2+x-1 then 1/alpha+1/beetaa. 1 b.2c. -1d.-1/2?.
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