Question

find the value of c such that equation 4x2 - 2(c + 1)x +(c + 4) = 0 has real and equal roots

Answer 1

X=7or X=-1 are the zeroes of the given quadratic equation

Answer 2

The value of "c is 5 or - 3".

Step-by-step explanation:

The given quadratic equation:

$4x^2-2(c+1)x+(c+4)=0$

To find the value of c = ?

Here, A = 4, B = - 2(c + 1) and C = c + 4

∴ D = $B^{2} -4AC$

= $(- 2(c + 1))^{2} -4(4)(c + 4)$

= $(4(c^2+2c+ 1)) -16(c + 4)$

$=4[(c^2+2c+ 1)) -4(c + 4)]$

∵ The roots are real and equal roots,

D ≥ 0

$4[(c^2+2c+ 1)) -4(c + 4)]=0$

⇒ $c^2+2c+ 1 -4c+16=0$

⇒ $c^2-2c-15=0$

⇒$c^2-5c+3c-15=0$

⇒$c(c-5)+3(c-5)=0$

⇒ $(c+3)(c-5)=0$

⇒ (c+3)(c-5)=0

∴ c = 5 or - 3

Hence,  the value of "c is 5 or - 3".