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 x^{2} 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,

ax^{2} + bx + c = 0, a ≠ 0

So, if coefficient of x^{2}(a) and constant term(c) have opposite signs then, the roots will always be real i.e.,

ac < 0

⇒ b^{2} - 4ac > 0

(vi) If the coefficient of x^{2} 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,

ax^{2} + bx + c = 0, a ≠ 0

So, if coefficient of x^{2}(a) and constant term(c) have the same sign and coefficient of x(b) is zero, then the roots will be imaginary.

ac > 0

⇒ b^{2} - 4ac < 0

Rate this question :

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