Question

If the equation 9x2 + 6kx + 4 = 0 has equal roots, then find the value of k

Answer 1

S O L U T I O N :

Given,

• Quadratic equation ; 9x² + 6kx + 4 = 0

To Find,

• The value of k.

Explanation,

Given, 9x² + 6kx + 4 = 0

On comparing with ax² + bx + c = 0 , We get ;

⟶ a = 9 , b = 6k , c = 4

Given, roots are real and equal,

Discriminate = 0

⟶ b² - 4ac = 0

[ Put the values ]

⟶ (6k)² - 4 × 9 × 4 = 0

⟶ 36k² - 36 × 4 = 0

⟶ 36k² - 144 = 0

⟶ 36k² = 144

⟶ k² = 144/36

⟶ k² = 4

⟶ k = ±√4

⟶ k = -2 OR k = 2

[ Note :- Ignoring negative term ]

⟶ k = 2

Therefore,

The value of k is 2.

Answer 2

Given, the roots of given quadratic equation are real and equal.

D= b²-4ac

36k²-4[4][9]

K²-4=0

K²=4

K=+-2