Question

For which values of c does the quadratic equation x^2-2x +c=0 have
two roots of the same sign

Answer 1

Answer: 0<c<1

Explanation:

If we are looking for roots with the same sign, we need to look at the discriminant, b^2 - 4ac, first. We do this because if the discriminant is positive we get two roots, and the question is asking us for two roots with the same sign.

Plugging in values, we get 4 - 4c > 0, and simplifying, we get:

4(1 - c) > 0

1 - c > 0

c < 1

Then, we can use Vieta's formula, which states that r1*r2 = c/a. Plugging in values we get:

r1*r2 = c

We want both roots to have the same sign, which means that c is positive, as two negative roots make a positive. This means that c is positive no matter what, thus making our other inequality, c > 0.