Q. 8

The zeroes of the quadratic polynomial x2 + kx + k where k≠0,
A. Cannot both be positive.

B. Cannot both be negative.

C. Are always unequal

D. Are always equal

Answer :

let p(x) = x2 + kx + k

x =


=


=


k (k - 4) > 0 k (- ∞, 0) (4, ∞)


Here k lies in two intervals, therefore we need to consider both the intervals separately.


Case1:


When k (- ∞, 0)


i.e. k < 0


we know that in a quadratic equation p(x) = ax2 + bx + c, if either a > 0, c < 0 or a < 0, c > 0, then the zeroes of the polynomial are of opposite signs.


Here a = 1 > 0, b = k < 0 and c = k < 0


both zeroes are of opposite signs


Case2:


When k (4, ∞)


i.e. k > 0


We know, in quadratic polynomial if the coefficients of the terms are of the same sign, then the zeroes of the polynomial are negative.


i.e. if either a > 0, b > 0 and c > 0 or a < 0, b < 0 and c < 0, then both zeroes are negative


Here a = 1 > 0, b = k > 0 and c = k > 0


both the zeroes are negative


Hence, by both cases, both the zeroes cannot be positive.

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
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
Solving Imp. Qs. of Olympiad on PolynomialsSolving Imp. Qs. of Olympiad on PolynomialsSolving Imp. Qs. of Olympiad on Polynomials47 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
Cubic PolynomialCubic PolynomialCubic Polynomial36 mins
Know the Relation Between Zero and CoefficientsKnow the Relation Between Zero and CoefficientsKnow the Relation Between Zero and Coefficients51 mins
Champ Quiz | Zero of a PolynomialChamp Quiz | Zero of a PolynomialChamp Quiz | Zero of a Polynomial30 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