Question

if the following quadratic equation has two equal and real root then find the value of k
(k+1)x^2-2(k+3)x+(2k+3)=0
step by step explain
it is urgent.. ​

Answer 1

=> To find Value Of K

=> x²-2(1+3k)x+7(3+2k) = 0

=> we know that D = b²-4ac and D = 0 If Roots are equal.......

Here a = 1 , b = -2(1+3k) , c = 7(3+2k)

=> substituting the values for D......

=> [-2(1+3k)]²-4(1){7(3+2k)}

=> 4(1+6k+9k²) - 4(21+14k) = 0

=>4[ 1+6k+9k²-21-14k] = 0

=> 4[ 9k² - 8k -20 ] = 0

=> Shifting 4 to L.H.S

=> 9k² -8k -20 = 0

=> Using Middle Term Split,

=> 9k²-18k+10k -20 = 0

=> 9k(k-2) + 10(k-2) = 0

=> (9k +10)(k-2) = 0

So, K = -10/9 , 2 Ans..