Question

Write whether the following statements are true or false. Justify your answers.
(i) Every quadratic equation has exactly one root.
(ii) Every quadratic equation has at least one real root.
(iii) Every quadratic equation has at least two roots.
(iv) Every quadratic equations has at most 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. (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.

NCERT Class X
Mathematics - Exemplar Problems

Chapter _QUADRATIC EQUATIONS

Answer 1

(i) False

⠀ Because a quadratic equation has ⠀⠀atmost two roots.

(ii) False

⠀⠀A quadratic equation has either two ⠀⠀real roots or no real roots.

(iii) False

⠀⠀Because quadratic equation has ⠀⠀atmost two roots.

(iv) True

⠀⠀ Because every quadratic equation ⠀⠀ has atmost two roots.

(v) True

⠀⠀Because in this case discriminant is ⠀⠀always positive, therefore it has real ⠀⠀roots, i.e, ac < 0 => b² - 4ac > 0

(vi) True

⠀⠀ Because in this case discriminant ⠀⠀is always negative, so it has no real ⠀⠀roots i.e., if b = 0 and ac > 0, then ⠀⠀ ⠀⠀b² - 4ac => - 4ac < 0.

Answer 2

Answer:

1. False 2.False 3.False 4.True 5.True