Question

ind the value of c such that the roots of quadratic equations are real and equal is 4x^2 -2(x+1)x+(c+4)

Answer 1

Question:

Find the value of c such that the roots of quadratic equations are real and equal is 4x^2 -2(x+1)x+(c+4)?

Answer:

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

$4 {x}^{2} - 2 {x}^{2} - 2x +c + 4$

$2 {x}^{2} - 2x + (c + 4)$

now , we know that the equation has equal and real roots

.°. it's discriminant must be zero

D = 0

$\implies$$d = {b}^{2} - 4ac = 0$

$\implies$${2}^{2} - 4(2)(c + 4) = 0$

$\implies$$4 - 8(c + 4) = 0$

$\implies$$- 8(c + 4) = 0$

$\implies$$c + 4 = 0$

$\implies$$c = ( - 4)$

Therefore , the value of $\huge \tt \underline \orange {c\:=\:-4}$