Question

1. State whether the following quadratic equations have two distinct real roots.

Justify your answer.

(i) x2

– 3x + 4 = 0 (ii) 2x2 + x – 1 = 0

(iii) 2x2

– 6x +

9

2 = 0 (iv) 3x2 – 4x + 1 = 0

(v) (x + 4) 2

– 8x = 0 (vi) (x – 2 )2

– 2(x + 1) = 0

(vii) 2 3 1 2 – 0

2 2

x x (viii) x (1 – x) – 2 = 0

(ix) (x – 1) (x + 2) + 2 = 0 (x) (x + 1) (x – 2) + x = 0

2. 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.​

Answer 1

Answer:

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