Q. 194.3( 30 Votes )

Find all the zero

Answer :

Let us assume f (x) = 2x4 – 11x3 + 7x2 + 13x - 7

As (3 + √2) and (3- √2) are the zeros of the given polynomial therefore each one of (x + 3 + √2) and (x + 3 - √2) is a factor of f (x)


Consequently, [(x – (3 + √2)][(x – (3 -√2)


= [(x – 3) - √2] [(x – 3) + √2]


= [(x – 3)2 – 2] = x2 – 6x + 7 is a factor of f (x)


Now, on dividing f (x) by (x2 – 6x + 7) we get:



f (x) = 0


2x4 - 11x3 + 7x2 + 13x – 7 = 0


(x2 - 6x + 7) (2x2 + x – 1) = 0


(x + 3 + √2) (x + 3 -√2) (2x – 1) (x + 1) = 0


x = - 3 - √2 or x = - 3 + √2 or x = 1/2 or x = - 1


Hence, all the zeros of the given polynomial are (-3 -√2), (-3 + √2), 1/2 and – 1

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
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
caricature
view all courses
RELATED QUESTIONS :

When a polynomialRS Aggarwal - Mathematics

Find all the zeroRD Sharma - Mathematics