Question

Find the value of k if the quadratic equation kx(x-2)+6=0 has equal roots

Answer 1

Heya !!!


KX(X-2) +6 = 0



KX² - 2KX +6 = 0




Here,



A1 = K , B1 = -2K and C = 6




Given that this equation have each Equal roots.



So,



Discriminant of the given equation should be 0.




Discriminant = 0




B² -4AC = 0


(-2K)² - 4 × K × 6 = 0



4K² - 24K = 0



4K² = 24K




4K²/K = 24


4K = 24



K = 24/4



K = 6.



Hence,



Value of K is 6.




HOPE IT WILL HELP YOU..... :-)

Answer 2

Hi,

Here is your answer,

→ kx(x-2)+6 = 0
→ kx²-2kx+6 = 0          { Spillting }
→ ax² + bx + c = 0

a = k , b = -2k, c = 6
Now,
We know that,

       ↔  b² -4ac = 0                  D = 0
→ (-2k)²-4(k)(6) = 0
→ 4k² - 24k = 0
→ 4k² = 24k
→ 4k²/k = 24       { Take k as common }
→ 4k = 24
→ k = 24/4
→ k = 6

Hope it helps you !