Question 330626
1.There are always two solutions to a quadratic equation. 
They may be a complex conjugate pair solution or a real solution, which includes the possibility of a double root at one x value. 
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2. Graphically, you can graph the function and see if it ever crosses the x axis. If it does, then the roots are real, if not, then the roots are complex.
Algebraically, use the discriminant, 
{{{D=b^2-4ac}}} where the quadratic equation is in the form {{{ax^2+bx+c=0}}}.
If {{{D>0}}}, two real distinct roots.
If {{{D=0}}}, one real double root.
If {{{D<0}}}, two complex conjugate pair roots.
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{{{graph(300,300,-10,10,-10,10,x^2+3x-10,(x-5)^2,x^2+x+2)}}}
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The red curve has two real roots, {{{y=x^2+3x-10}}}, {{{D=9+40=49}}}
The green curve has one real double root, {{{y=x^2-10x+25}}},{{{D=100-100=0}}}
The blue curve has complex conjugate roots, {{{y=x^2+x+2}}},{{{D=1-8=-7}}}