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Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, − 7, − 14 respectively - Mathematics

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Question

Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, − 7, − 14 respectively

Solution

Let the polynomial be ax3 + bx+ cx + d and the zeroes be α, β and γ

Then, α + β + γ = `(2)/1 = (-b)/a`

αβ + βγ + γα = `(-7)/1 = c/a`

αβγ = `(-14)/1 = (-d)/a`

∴ a = 1, b = -2, c = -7 and d = 14

Hence, the polynomial is  x3 - 2x2  - 7x + 14

  Is there an error in this question or solution?
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APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 10 (2019 (Latest))
Chapter 2: Polynomials
Ex. 2.4 | Q: 2 | Page no. 36
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Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, − 7, − 14 respectively Concept: Relationship Between Zeroes and Coefficients of a Polynomial.
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