Question

5. Find the value ofc for which the quadratic
equation, 4x²2(c+1) x+(x+1)=0has equal
roots
​

Answer 1

Answer:

Given equation is 4x²+ 2(c+1)x+ 1

Here, a= 4, b= 2(c+1)= 2c+2 and c =1

Now, since the equation has equal roots

therefore, b²-4ac= 0

=> (2c+2)²- 4×4×1= 0

=> 4c²+8c+4- 16= 0

=> 4c²+8c-12=0

=> c²+2c-3= 0

=> c²+ 3c - c-3= 0

=> c(c+3) -1(c+3)=0

=> (c+3)(c-1)=0

either, c+3=0 or, c-1=0

=> c= -3 => c= 1

thus, the required values of C are -3 and 1.