Question

If the equation 9x² + 6kx + 4 = 0 has equal roots, then the roots are both equal to

विकल्प

• ± `2/3`

• ± `3/2`

• 0

• ±3

Answer 1

Given, quadratic equation is: 9x² + 6kx + 4 = 0 

 Now, the given equation has equal roots, so D = 0

⇒ b² - 4ac = 0

⇒ (6k)² - 4 × 9 × 4 = 0

⇒ 36k² - 36 × 4 = 0

⇒ 36k² = 36 × 4

⇒ k² = 4

⇒ k = ± 2

Case 1: When k = 2, we have the quadratic equation as:

9x² + 6(2)x + 4 = 0

⇒ 9x² + 12x + 4 = 0

⇒ (3x)² + 2 × 2 × 3x + (2)² = 0

⇒ (3x + 2)² = 0

⇒ 3x + 2 = 0

⇒ x = -`2/3`

Case 2: When k = -2, we have the quadratic equation as:

9x² + 6(-2)x + 4 = 0

⇒ 9x² - 12x + 4 = 0

⇒ (3x)² - 2 × 2 × 3x + (2)² = 0

⇒ (3x - 2)² = 0

⇒ 3x - 2 = 0

⇒ x = `2/3`

So, two roots of the quadratic equation are `2/3 and -2/3 or ±2/3`.