Consider $$(k-1)x^2+2x+k=0.$$ Find all $k$ for which the equation has exactly one distinct real so

Question

Consider $$(k-1)x^2+2x+k=0.$$ Find all $k$ for which the equation has exactly one distinct real solution. Explain why using only $\Delta=0$ would miss an answer.

Accepted Answer

$k=1,\ \frac{1-\sqrt5}{2},\ \frac{1+\sqrt5}{2}$

Quadratic Functions, Equations and Inequalities

Quadratic Functions, Equations and Inequalities

Solution:

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