Class 10 Exam > Class 10 Questions > Given that two of the zeros of the cubic poly...
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Given that two of the zeros of the cubic polynomial ax3 + bx2 + cx + d are 0, the value of c is
- a)less than 0
- b)greater than 0
- c)equal to 0
- d)can’t say
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Given that two of the zeros of the cubic polynomial ax3 + bx2 + cx + d...
Explanation:
Given Information:
- Two zeros of the cubic polynomial are 0.
- Therefore, the cubic polynomial can be written as ax^3 + bx^2 + cx + d = a(x - 0)(x - 0)(x - k) = ax^3 - akx^2 = ax^3.
Finding the value of c:
- Since the coefficient of the linear term in the polynomial is c, and two of the zeros are given to be 0, the sum of the zeros is 0 + 0 + k = -b/a.
- As k represents the remaining zero, this implies that k = -b/a.
- Since the sum of the zeros of a cubic polynomial is -b/a, the value of c cannot be determined from the given information.
- Therefore, the correct answer is c.
Given Information:
- Two zeros of the cubic polynomial are 0.
- Therefore, the cubic polynomial can be written as ax^3 + bx^2 + cx + d = a(x - 0)(x - 0)(x - k) = ax^3 - akx^2 = ax^3.
Finding the value of c:
- Since the coefficient of the linear term in the polynomial is c, and two of the zeros are given to be 0, the sum of the zeros is 0 + 0 + k = -b/a.
- As k represents the remaining zero, this implies that k = -b/a.
- Since the sum of the zeros of a cubic polynomial is -b/a, the value of c cannot be determined from the given information.
- Therefore, the correct answer is c.
This question is part of UPSC exam. View all Class 10 courses
Most Upvoted Answer
Given that two of the zeros of the cubic polynomial ax3 + bx2 + cx + d...
Solun : Let p,q and r be zeros of given polynomial such that p = 0 and q = 0.
We know that , pq + qr + rp = c/a
---> 0×0 + 0×r + r×0 = c/a
---> 0 = c/a
---> c = 0
Hence, option C is correct.
We know that , pq + qr + rp = c/a
---> 0×0 + 0×r + r×0 = c/a
---> 0 = c/a
---> c = 0
Hence, option C is correct.
Community Answer
Given that two of the zeros of the cubic polynomial ax3 + bx2 + cx + d...
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Given that two of the zeros of the cubic polynomial ax3 + bx2 + cx + d are 0, the value of c isa)less than 0b)greater than 0c)equal to 0d)can’t sayCorrect answer is option 'C'. Can you explain this answer?
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