Question

10 points for clear answer ​

Answer 1

Answer:

0 or 4

Step-by-step explanation:

  For an equation to have equal roots, discriminant must be 0.

Discriminant for ax^2 + bx + c = 0 is given by b^2 - 4ac.

 Here, b = - 3k, a = 9 , c = k

⇒ Discriminant = 0

⇒ ( - 3k )^2 - 4( 9 * k ) = 0

⇒ 9k^2 - 36k = 0

⇒ k( 9k - 36 ) = 0

⇒ k = 0  or 9k - 36 = 0

⇒ k = 0 or k = 36/9

⇒ k = 0 or k = 4

Answer 2

Answer:

Given quadratic equation : 9x² - 3kx + k = 0

We know that

For a quadratic equation which is having equal roots discriminant must be 0

Discriminant ( ∆ ) = b² - 4ac = 0

Where

• a : coefficient of x² = 9
• b : coefficient of x = - 3k
• c : constant term = k

To find: k = ?

Substituting the values of a ,b ,c

→ ∆ = ( -3k )² - 4( 9 )( k )

→ 0 = 9k² - 36k

Taking common

→ 9k( k - 4 ) = 0

♦ 9k = 0

♦ k = 0

_________________

♦ k - 4 = 0

♦ k = 4

_________________

Hence, k = 0 or 4