Q3Multiple choiceExercise 4.2
1 (vii) 2 x2 – x + = 0 (viii) x (1 – x) – 2 = 0 2 2 (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. QUADRATIC EQUATIONS 39 (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. 3. A quadratic equation with integral coefficient has integral roots. Justify your answer.
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x2–3x + 1 = 0 is an equation with integral coefficients but its roots are not integers.