Question

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

Answer 1

Answer:

c > 1

Step-by-step 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:

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

$\implies 4-4c < 0$

$\implies 4 < 4c$

$\implies 1 < c$

$\implies c > 1$

Answer 2

Here

• a=1
• b=-2

Discriminant must be less than 0

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

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

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

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

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

$\\ \rm\Rrightarrow 1<c$

$\\ \rm\Rrightarrow c>1$