Question

find the value of k for equal roots in quadratic equation x2-2x(1+3k)+7(3+2k)=0

Answer 1

hello users ......

we have given equation is  
x² + 2x(1 + 3k) +7(3 + 2k) = 0 
or 
x² + 2(1 + 3k)x +7(3 + 2k) = 0 

roots are equal 
we have to find the value of k =? 

now 
we know that an equation have equal roots if and only if D = 0
=> b² -4ac = 0 

here comparing the equation with 
ax² + bx + c = 0 

here 
a= 1, b =  2(1 + 3k) and c=  7(3 + 2k) 

now 
   b² - 4ac = 0
 
=  [ 2(1 + 3k) ]² - 4 ×1×7(3 + 2k)  = 0 
= 4×(1 + 3k)² - 4×7(3 + 2k) = 0
 = 4(1 + 9k² + 6k) - 4(21 +14k) =0
= (1 + 9k² + 6k) - (21 +14k) =0
=> 9k² - 8k -20 = 0 

   now solving the equation we get 
= 9k² - 18k + 10k - 20 = 0
= 9k( k- 2)  + 10(k -2) =0 
=> 9k +10=0 and k -2 = 0
=> k = -10/9 and 2 answer 

✯✯ hope it helps ✯✯

Answer 2

Answer:

k = 2

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