Question -
Answer -
- Every quadratic equation has exactly one root.
- Every quadratic equation has at least one real root.
- Every quadratic equation has at least two roots.
- Every quadratic equations has at most two roots.
- If the coefficient of x2 and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots.
- 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.
Solution:
(i)False. For example, a quadratic equation x2 – 9 = 0has two distinct roots – 3 and 3.
(ii) False. For example, equation x2 +4 = 0 has no real root.
(iii) False. For example, a quadraticequation x2 – 4x + 4 = 0 has only oneroot which is 2.
(iv) True, because every quadratic polynomialhas almost two roots.
(v) True, because in this case discriminant isalways positive.
For example, in ax2+ bx + c =0, as a and c have opposite sign, ac <0
⟹ Discriminant = b2 – 4ac >0.
(vi) True, because in this case discriminantis always negative.
For example, in ax2+ bx + c =0, as b = 0, and a and c havesame sign then ac > 0
⟹ Discriminant = b2 – 4ac =– 4 a c < 0