Share

# 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 - CBSE Class 10 - Mathematics

ConceptRelationship Between Zeroes and Coefficients of a Polynomial

#### 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?

#### APPEARS IN

NCERT Solution for Mathematics Textbook for Class 10 (2019 to Current)
Chapter 2: Polynomials
Ex. 2.40 | Q: 2 | Page no. 36

#### Video TutorialsVIEW ALL [2]

Solution 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.
S