Q. 54.0( 9 Votes )

If α and β are the zeros of the polynomial f(x) = x2 + px + q, then a polynomial having and is its zeros is
A. x2 + qx + p

B. x2 – px + q

C. qx2 + px + 1

D. px2 + qx + 1

Answer :

Given: If α and β are the zeros of the polynomial f(x) = x2 + px + q,

To find: a polynomial having and is its zeros is


Solution:

f(x) = x2 + px + q


We know,





Since α, β are zeroes of given polynomial,

⇒ α + β = – p


and αβ = q


Let S and P denote respectively the sum and product of zeroes of the required polynomial,

So,

 

...... (1)

And

...... (2)



Put the values of 
α + β  and αβ in (1) and (2) to get,



And



We know equation having 2 zeroes is of form,

k (x2 - (sum of zeroes) x + product of zeroes) 

For a polynomial having and is its zeros the equation becomes,


 x2 + p/q x + 1/q = 0


So here we get,


g(x) = qx2 + px + 1

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 CoefficientsChamp Quiz |Revealing the relation Between Zero and CoefficientsChamp Quiz |Revealing the relation Between Zero and Coefficients38 mins
Relation Between zeroes and CoefficientsRelation Between zeroes and CoefficientsRelation Between zeroes and Coefficients46 mins
Interactive Quiz - Geometrical Meaning of the ZeroesInteractive Quiz - Geometrical Meaning of the ZeroesInteractive Quiz - Geometrical Meaning of the Zeroes32 mins
Relationship between Zeroes and Coefficients-2Relationship between Zeroes and Coefficients-2Relationship between Zeroes and Coefficients-238 mins
Quiz - Division AlgorithmQuiz - Division AlgorithmQuiz - Division Algorithm38 mins
Relationship between Zeroes and Coefficients-1Relationship between Zeroes and Coefficients-1Relationship between Zeroes and Coefficients-152 mins
Interactive Quiz:PolynomialsInteractive Quiz:PolynomialsInteractive Quiz:Polynomials43 mins
Division Algorithm-1Division Algorithm-1Division Algorithm-130 mins
Relation b/w The Zeroes and Coefficients of Cubic PolynomialsRelation b/w The Zeroes and Coefficients of Cubic PolynomialsRelation b/w The Zeroes and Coefficients of Cubic Polynomials54 mins
Revision of Relation Between the Zeroes and Coefficients of Quadratic PolynomialRevision of Relation Between the Zeroes and Coefficients of Quadratic PolynomialRevision of Relation Between the Zeroes and Coefficients of Quadratic Polynomial46 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
caricature
view all courses