- #1

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- Homework Statement
- The equation 2x^2 - 2(2a + 1)x + a(a - 1) = 0 has two real roots x1 and x2. Find a such that x1 < a < x2 !

- Relevant Equations
- Discriminant

Quadratic formula

For quadratic equation to have two real roots:

b

(-2 (2a + 1))

4 (4a

16a

8a

2a

Using quadratic formula, I get a < (-3 - √7) / 2 or a > (-3 + √7) / 2

Then how to know if a is between x

b

^{2}- 4ac > 0(-2 (2a + 1))

^{2}- 4 (2) (a (a - 1)) > 04 (4a

^{2}+ 4a + 1) - 8a^{2}+ 8a > 016a

^{2}+ 16a + 4 - 8a^{2}+ 8a > 08a

^{2}+ 24 a + 4 > 02a

^{2}+ 6a + 1 > 0Using quadratic formula, I get a < (-3 - √7) / 2 or a > (-3 + √7) / 2

Then how to know if a is between x

_{1}and x_{2}? Thanks