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If one root of polynomial equation ax2 + bx + c = 0 be reciprocal of other, then
- a)b = 0
- b)b = c
- c)a = 0
- d)a = c
Correct answer is option 'D'. Can you explain this answer?
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Solution:
Given, the roots of the quadratic equation ax2 + bx + c = 0 are reciprocal of each other.
Let the roots be p and q, then q = 1/p.
We know that the sum of roots of a quadratic equation is given by -b/a and the product of roots is given by c/a.
Therefore, p + q = p + 1/p = -b/a and pq = p(1/p) = 1/a
Multiplying both sides of pq = 1/a by a, we get p = 1/aq.
Substituting p = 1/aq in p + q = -b/a, we get 1/aq + q = -b/a.
Multiplying both sides by aq, we get 1 + aq2 = -bq.
Rearranging the terms, we get aq2 + bq + 1 = 0.
This is a quadratic equation in q and we know that p and q are the roots of the given quadratic equation.
Since the roots are reciprocal of each other, we have p = 1/q.
Substituting p = 1/q in the given quadratic equation, we get a/q2 - bq + 1 = 0.
Multiplying both sides by q2, we get a - bq2 + q2 = 0.
Multiplying both sides by -1, we get bq2 - a - q2 = 0.
Comparing the coefficients of q2, we get b = 0 and comparing the constant terms, we get a = c.
Therefore, the correct answer is option D, which states that a = c.
Given, the roots of the quadratic equation ax2 + bx + c = 0 are reciprocal of each other.
Let the roots be p and q, then q = 1/p.
We know that the sum of roots of a quadratic equation is given by -b/a and the product of roots is given by c/a.
Therefore, p + q = p + 1/p = -b/a and pq = p(1/p) = 1/a
Multiplying both sides of pq = 1/a by a, we get p = 1/aq.
Substituting p = 1/aq in p + q = -b/a, we get 1/aq + q = -b/a.
Multiplying both sides by aq, we get 1 + aq2 = -bq.
Rearranging the terms, we get aq2 + bq + 1 = 0.
This is a quadratic equation in q and we know that p and q are the roots of the given quadratic equation.
Since the roots are reciprocal of each other, we have p = 1/q.
Substituting p = 1/q in the given quadratic equation, we get a/q2 - bq + 1 = 0.
Multiplying both sides by q2, we get a - bq2 + q2 = 0.
Multiplying both sides by -1, we get bq2 - a - q2 = 0.
Comparing the coefficients of q2, we get b = 0 and comparing the constant terms, we get a = c.
Therefore, the correct answer is option D, which states that a = c.
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If one root of polynomial equation ax2+ bx + c = 0 be reciprocal of other, thena)b = 0b)b = cc)a = 0d)a = cCorrect answer is option 'D'. Can you explain this answer? 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 one root of polynomial equation ax2+ bx + c = 0 be reciprocal of other, thena)b = 0b)b = cc)a = 0d)a = cCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If one root of polynomial equation ax2+ bx + c = 0 be reciprocal of other, thena)b = 0b)b = cc)a = 0d)a = cCorrect answer is option 'D'. Can you explain this answer?.
If one root of polynomial equation ax2+ bx + c = 0 be reciprocal of other, thena)b = 0b)b = cc)a = 0d)a = cCorrect answer is option 'D'. Can you explain this answer? 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 one root of polynomial equation ax2+ bx + c = 0 be reciprocal of other, thena)b = 0b)b = cc)a = 0d)a = cCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If one root of polynomial equation ax2+ bx + c = 0 be reciprocal of other, thena)b = 0b)b = cc)a = 0d)a = cCorrect answer is option 'D'. Can you explain this answer?.
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