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The number of polynomials having zeros as - 2 and 5 is
- a)1
- b)2
- c)3
- d)more than 3
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The number of polynomials having zeros as - 2 and 5 isa)1b)2c)3d)more ...
let - 2 and 5 are the zeroes of the polynomials of the formp(x) = ax^2 + bx + c.
sum of the zeroes = - (coefficient of x) � coefficient of x^2 i.e.
Sum of the zeroes = - b/a
- 2 + 5 = - b/a
3 = - b/a
⇒ b = - 3 and a = 1
Product of the zeroes = constant term � coefficient of x^2 i.e.
Product of zeroes = c/a
(- 2)5 = c/a
- 10 = c
Put the values of a, b and c in the polynomial p(x) = ax^2 + bx + c.
∴ The equation is x^2 - 3x - 10
OR
The equation of a quadratic polynomial is given by x^2 - (sum of the zeroes)x + (product of the zeroes) where,
Sum of the zeroes = - (coefficient of x) � coefficient of x^2 and
Product of the zeroes = constant term � coefficient of x^2
∴ Sum of the zeroes = - 2 + 5 and product of the zeroes = (- 2)5
= 3 = - 10
∴ the equation is x^2 - 3x - 10
We know, the zeroes do not change if the polynomial is divided or multiplied by a constant
⇒ kx^2 - 3kx - 10k will also have - 2 and 5 as their zeroes.
As k can take any real value, there can be many polynomials having - 2 and 5 as their zeroes.
Most Upvoted Answer
The number of polynomials having zeros as - 2 and 5 isa)1b)2c)3d)more ...
Solution:
Given, the zeros of the polynomial are -2 and 5.
Let the polynomial be p(x)
So, p(-2) = 0 and p(5) = 0
Therefore, (x+2) and (x-5) are the factors of the polynomial p(x).
Hence, p(x) = (x+2)(x-5)q(x) where q(x) is a polynomial.
Therefore, the number of polynomials that can be formed by multiplying (x+2) and (x-5) with different polynomials q(x) is more than 3.
Hence, the correct answer is option 'D'.
Given, the zeros of the polynomial are -2 and 5.
Let the polynomial be p(x)
So, p(-2) = 0 and p(5) = 0
Therefore, (x+2) and (x-5) are the factors of the polynomial p(x).
Hence, p(x) = (x+2)(x-5)q(x) where q(x) is a polynomial.
Therefore, the number of polynomials that can be formed by multiplying (x+2) and (x-5) with different polynomials q(x) is more than 3.
Hence, the correct answer is option 'D'.
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Community Answer
The number of polynomials having zeros as - 2 and 5 isa)1b)2c)3d)more ...
Option d is correct. .
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The number of polynomials having zeros as - 2 and 5 isa)1b)2c)3d)more than 3Correct answer is option 'D'. Can you explain this answer?
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The number of polynomials having zeros as - 2 and 5 isa)1b)2c)3d)more than 3Correct answer is option 'D'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The number of polynomials having zeros as - 2 and 5 isa)1b)2c)3d)more than 3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of polynomials having zeros as - 2 and 5 isa)1b)2c)3d)more than 3Correct answer is option 'D'. Can you explain this answer?.
The number of polynomials having zeros as - 2 and 5 isa)1b)2c)3d)more than 3Correct answer is option 'D'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The number of polynomials having zeros as - 2 and 5 isa)1b)2c)3d)more than 3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of polynomials having zeros as - 2 and 5 isa)1b)2c)3d)more than 3Correct answer is option 'D'. Can you explain this answer?.
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