Question

Find the values of c for which the quadratic equation 4x square - 2(c+1)x+(c+1)=0 has equal roots

Answer 1

4x2 - 2(c+1)x +(c+4) =0

using quadratic formula

a = 4x2 = 8

b = -2(c+1)

c = (c+4)

D = b2 - 4ac

= 4(c+1)2 - 4(c+4) (8)

= 4 (c2 +2c +1) - 32(c+4)

= 4c2 +8c +4 -32c-128

= 4c2 - 24c - 124

4c2 - 24c -124 =0 (since the roots are real and equal b2-4ac = 0)

divide by 4

c2 -6c - 31 =0

a=1 b= -6 c= -31

D = b2- 4ac

= 36 - 4 (-31)

= 36 + 124

=160 (root of 160 = 40)

c = 6 + 40 / 2

= 46/2

=23

c = 6 - 40/2

= -34 /2

= --17

c can be -17 or 23

Answer 2

the answer is -17 or 23