Q. 11 D5.0( 1 Vote )

# Verify that the numbers given alongside of the cubic polynomial are their zeros. Also verify the relationship between the zeroes and the coefficients in each case :x3 + 5x2 + 7x + 3 ; – 3, 2 – 1, – 1

Let p(x) = x3 + 5x2 + 7x + 3.

Then, p( – 1) = ( – 1)3 + 5( – 1)2 + 7( – 1) + 3

= – 1 + 5 – 7 + 3

= 0
p( – 3) = ( – 3)
3 + 5( – 3)2 + 7( – 3) + 3

= – 27 + 45 – 21 + 3

= 0

Hence, – 1, – 1 and – 3 are the zeroes of the given polynomial x3 + 5x2 + 7x + 3.

Now, Let α = – 1 , β = – 1 and γ = – 3

Then, α + β + γ = – 1 + ( – 1) + ( – 3) = – 5

αβ + βγ + γα = ( – 1)( – 1) + ( – 1)( – 3) + ( – 3)( – 1)

= 1 + 3 + 3

= 7

and αβγ = ( – 1) × ( – 1) × ( – 3)

= – 3

Thus, the relationship between the zeroes and the coefficients is verified.

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:Polynomials43 mins
Division Algorithm-130 mins
Relation b/w The Zeroes and Coefficients of Cubic Polynomials54 mins
Revision of Relation Between the Zeroes and Coefficients of Quadratic Polynomial46 mins
Solving Imp. Qs. of Olympiad on Polynomials47 mins
Interactive Quiz - Geometrical Meaning of the Zeroes32 mins
Relationship between Zeroes and Coefficients-238 mins
Cubic Polynomial36 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