Q1 of 51 Page 38

State whether the following quadratic equations have two distinct real roots. Justify your answer.

(x - 1) (x + 2) + 2 = 0

The equation (x - 1) (x + 2) + 2 = 0 has two real and distinct roots.


Simplifying the above equation,


⇒ x2 – x + 2x – 2 + 2 = 0


∴ x2 + x = 0


∴ D = b2 - 4ac


= 12 - 4(1)(0)


= 1 - 0 > 0


Hence, the roots are real and distinct.


More from this chapter

All 51 →
1

State whether the following quadratic equations have two distinct real roots. Justify your answer.

 1

State whether the following quadratic equations have two distinct real roots. Justify your answer.

x (1 - x) – 2 = 0

 1

State whether the following quadratic equations have two distinct real roots. Justify your answer.

(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 equation 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.