Question

For what values of c does the equation c-2)x^2+2(c-2)+2=0 possess no real roots

Answer 1

Answer:

The quadratic equation has no real roots if its discriminant is less than zero i.e D<0

⇒b

2

−4ac<0

⇒(2(c−2))

2

−4×(c−2)×(−2)<0

⇒4(c

2

+4−4c)+4c−16<0

⇒ 4c

2

+16−16c+4c−16<0

⇒ 4c

2

−12c<0

⇒ 4c

2

−12c<0

⇒ (4c)(c−3)<0

⇒ c−3<0

⇒ c>0 and c−3<0 or c<0 and c−3>0

⇒ c<0 and c<3

Hence, c∈(0,3)

Answer 2

Step-by-step explanation:

⇒ b

2

<4ac

⇒ [2(C−2)]

2

<4(C−2)(2)

⇒ 4(C−2)

2

<4(2)(C−2)

⇒ (C−2)

2

<2(C−2)

⇒ (C−2)(C−2−2)<0

⇒ (C−2)(C−4)<0

C should be between 2 and 4

⇒ C=3

∴ if C=3

(C−2)x

2

+2(C−2)x+2=0 will have no real roots.