Question

find the value of k, in the quadratic equation kx^2 - 2√3kx + 9 = 0 has equal roots?​

Answer 1

Answer:

K=3

Step-by-step explanation:

Since given that has real and equal roots

Answer 2

Given :   quadratic equation kx^2 - 2√3kx + 9 = 0 has equal roots​

To find : value of k

Solution:

any Quadratic equation

ax² + bx + c = 0

has equal roots

if  d = 0

if b² - 4ac = 0

now comparing

kx² - 2√3kx + 9 = 0

with ax² + bx + c = 0

a = k  

b = - 2√3k

c = 9

=> (-2√3k)² - 4k(9) = 0

=> 12k² - 36k  = 0

=> 12k² = 36k

=> k = 3

for Value of k = 3  the  quadratic equation kx² - 2√3kx + 9 = 0  has equal roots

Verification :

3x² - 6√3x  + 9 = 0

=> x² - 2√3x + 3 = 0

=> (x - √3)² = 0

=> x = √3

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