SOLUTION: Please help me answer this: show that m(x^2-x)+1-m=x^2 has real roots for all real values of m. (P.S. Do forgive me for all the inconvenience.)

Question 948575: Please help me answer this: show that m(x^2-x)+1-m=x^2 has real roots for all real values of m. (P.S. Do forgive me for all the inconvenience.)
Answer by josgarithmetic(39625) (Show Source): You can put this solution on YOUR website!

Quadratic equation with "unknown" x, and constant m.
Real roots? Discriminant must be non-negative.

, the given equation now in general form.

Inequality for the discriminant needed:
, left member is the discriminant.

The truth of this m inequality depends on no real roots for m, meaning the discriminant of just the m inequality must be NEGATIVE.
If , then the m quadratic inequality has no real roots.

------TRUE.

That truth means that the is satisfied; and that means that the original given equation will have real roots (for all m).
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