Q. 2 E5.0( 4 Votes )

# Are the following statements ‘true’ or ‘False’? Justify your answer.If all the zeroes of a cubic polynomial are negative, then all the coefficients and the constant term of the polynomial have the same sign.

If all the zeroes of a cubic polynomial are negative, then all the coefficients and the constant term of the polynomial have the same sign: True

Let α, β and γ be the zeroes of the polynomial p(x) = ax3 + bx2 + cx + d, where α, β, γ < 0

Product of all zeroes = - (constant term) ÷ coefficient of x3

αβγ = - d/a < 0 ( α, β, γ < 0 αβγ < 0)

d/a > 0

d and a have the same signs.

Sum of the products of two zeroes at a time = coefficient of x ÷ coefficient of x3

αβ + βγ + αγ = c/a > 0 ( α, β, γ < 0 αβ,βγ,αγ > 0 αβ + βγ + αγ > 0 )

c and a have the same signs.

Sum of the zeroes = - (coefficient of x2) ÷ coefficient of x3

α + β + γ = - b/a < 0 ( α, β, γ < 0 α + β + γ < 0)

b/a > 0

b and a have same signs.

a,b,c and d have same signs.

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
Interactive Quiz:Polynomials43 mins
Division Algorithm-130 mins
Relation b/w The Zeroes and Coefficients of Cubic Polynomials54 mins
Solving Imp. Qs. of Olympiad on Polynomials47 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