If-the-quadratic-equation-x-2-2x-m-1-0-has-two-different-positive-real-roots-Determine-the-range-of-m-For-example-0-lt-m-lt-3-or-I-will-force-you-to-determine-

Question Number 215167 by MathematicalUser2357 last updated on 30/Dec/24

If the quadratic equation x^{2} - 2 x - m + 1 = 0 has two different positive real roots α, β,

Determine the range of m (For example, 0 < m < 3) or I will force you to determine

Answered by A5T last updated on 30/Dec/24

x_{1, 2} = \frac{2 \underline{+} \sqrt{4 - 4 (1 - m)}}{2} = 1 \underline{+} \sqrt{m}

m > 0 \land 1 - \sqrt{m} > 0 \Rightarrow m > 0 \land m < 1

\Rightarrow 0 < m < 1

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