Short Answer Questions 2 — Question 5

(a) Given, equation : 5𝑥² − 9𝑥 + 4 = 0

Comparing above equation with ax² + bx + c = 0, we get :

a = 5, b = -9 and c = 4.

Discriminant (D) = b² - 4ac = (-9)² - 4 × 5 × 4 = 81 - 80 = 1.

Since, D > 0 and a perfect square.

Hence, equation 5𝑥² − 9𝑥 + 4 = 0 has real roots.

(b) Solving,

⇒ 5𝑥² − 9𝑥 + 4 = 0

⇒ 5x² - 5x - 4x + 4 = 0

⇒ 5x(x - 1) - 4(x - 1) = 0

⇒ (5x - 4)(x - 1) = 0

⇒ 5x - 4 = 0 or x - 1 = 0

⇒ 5x = 4 or x = 1

⇒ x = $\dfrac{4}{5}$ or x = 1.

Hence, roots of the equation are 1 and $\dfrac{4}{5}$.