Question

For which values of c does the quadratic equation x^(2)-2x+c=0 have No real roots?

Answer 1

Here

• a=1
• b=-2

Discriminant must be less than 0

`\\ \rm\Rrightarrow b^2-4ac<0`

`\\ \rm\Rrightarrow (-2)^2-4(1)(c<0`

`\\ \rm\Rrightarrow 4-4c<0`

`\\ \rm\Rrightarrow 4(1-c)<0`

`\\ \rm\Rrightarrow 1-c<0`

`\\ \rm\Rrightarrow 1<c`

`\\ \rm\Rrightarrow c>1`

Answer 2

c > 1

Explanation:

Given equation:
`x^2-2x+c=0`

General form of quadratic equation:
`ax^2+bx+c=0`

We can use the discriminant to determine the value of c for which the equation has no real roots.

`b^2-4ac < 0\implies \textsf{no real roots}`

From the given equation:

• 
  `a=1`
• 
  `b=-2`
• 
  `c=c`

Inputting these values into the discriminant formula:

`\implies (-2)^2-4(1)(c) < 0`

`\implies 4-4c < 0`

`\implies 4 < 4c`

`\implies 1 < c`

`\implies c > 1`