# Find a cubic polynomial whose zeroes are 0, 1, 2.

A cubic polynomial having α, β, and γ as zeroes is given by,

P(x) = x3 – (α + β + γ)x2 + (αβ + βγ + γα)x – (αβγ)

Explanation:

α + β + γ = 0 + 1 + 2 = 3

αβ + βγ + γα = 0 × 1 + 1 × 2 + 2 × 0

αβ + βγ + γα = 0 + 2 + 0 = 2

αβγ = 0 × 1 × 2 = 0

Putting the values, we get,

P(x) = x3 – (3)x2 + (2)x – (0)

P(x) = x3 – 3x2 + 2x

Therefore, P(x) = x3 – 3x2 + 2x

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Champ Quiz |Revealing the relation Between Zero and Coefficients38 mins
Relation Between zeroes and Coefficients46 mins
Interactive Quiz - Geometrical Meaning of the Zeroes32 mins
Relationship between Zeroes and Coefficients-238 mins
Relationship between Zeroes and Coefficients-152 mins
Quiz - Division Algorithm38 mins
Relation b/w The Zeroes and Coefficients of Cubic Polynomials54 mins
Revision of Relation Between the Zeroes and Coefficients of Quadratic Polynomial46 mins
Interactive Quiz:Polynomials43 mins
Division Algorithm-130 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses