Question

fin the value of k for which the roots are real and equal

Answer 1

Hi !

a quadratic equation is of the form ax² + bx + c = 0
If the roots are real and equal  then, b² - 4ac = 0

(i) x² - 2kx + 7k- 12 = 0
a = 1 , b = -2k  , c = 7k - 12

b² - 4ac
 (-2k)² - 4*(7k - 12) = 0
4k² - 28k + 48 = 0
 k² - 7k + 12 = 0
k²- 3k - 4k + 12= 0 
k(k - 3) - 4(k - 3) = 0 
(k - 3) (k - 4) = 0 
k - 3 = 0 , k - 4 = 0 
k = 3 , k = 4

Hence, the value(s) of k are 3 and 4.
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(ii) kx(x - 2√5) + 10 = 0

kx² - 2√5kx + 10 = 0

a = k , b = -2√5k , c = 10

b² - 4ac = 0

(-2√5k)² - 4*k*10 = 0 

20k² - 40k = 0

20k² = 40k

Cancelling "k" on both sides,

20k = 40

k = 40/20
  
   = 2

The value of k is 2