Q. 23.8( 13 Votes )

Write whether the

Answer :

(i) Every quadratic equation has exactly one root: False


A quadratic equation has exactly two roots.


(ii) Every quadratic equation has at least one real root: False


A quadratic equation may have real or imaginary roots.


(iii) Every quadratic equation has at least two roots: False


A quadratic equation has exactly two roots, no more no less.


(iv) Every quadratic equation has at most two roots: True


A quadratic equation can’t have more than two roots.


(v) If the coefficient of x2 and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots: True


The standard form of a quadratic equation is given by,


ax2 + bx + c = 0, a ≠ 0


So, if coefficient of x2(a) and constant term(c) have opposite signs then, the roots will always be real i.e.,


ac < 0


b2 - 4ac > 0


(vi) If the coefficient of x2 and the constant term have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real roots: True


The standard form of a quadratic equation is given by,


ax2 + bx + c = 0, a ≠ 0


So, if coefficient of x2(a) and constant term(c) have the same sign and coefficient of x(b) is zero, then the roots will be imaginary.


ac > 0


b2 - 4ac < 0


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 :

Which of the follRS Aggarwal - Mathematics

Solve each of theRS Aggarwal - Mathematics

Solve each of theRS Aggarwal - Mathematics

Solve each of theRS Aggarwal - Mathematics

Solve each of theRS Aggarwal - Mathematics