Let $$\mathrm{f}(x)=x^2-2x+3.$$ Complete the square and show that $\mathrm{f}(x)0$ for every r

Question

Let $$\mathrm{f}(x)=x^2-2x+3.$$ Complete the square and show that $\mathrm{f}(x)>0$ for every real $x$. Confirm this using the discriminant. Hence solve $x^2-2x+3\leq0$.

Accepted Answer

(a) $\mathrm{f}(x)=(x-1)^2+2\geq2>0$, (b) $\Delta=-8$; (c) No solutions to $\mathrm{f}(x)\leq0$.

Quadratic Functions, Equations and Inequalities

Quadratic Functions, Equations and Inequalities

Solution:

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