SOLUTION: Hi please help me graph these polynomial inequalities. Thank you very much! a. {{{ 25x^2-10x+1<0 }}} b. {{{ 25x^2-10x+1<=0 }}} c. {{{ 25x^2-10x+1>0 }}} d. {{{ 25x^2-10x

Algebra ->  Graphs -> SOLUTION: Hi please help me graph these polynomial inequalities. Thank you very much! a. {{{ 25x^2-10x+1<0 }}} b. {{{ 25x^2-10x+1<=0 }}} c. {{{ 25x^2-10x+1>0 }}} d. {{{ 25x^2-10x      Log On


   

Question 1052831: Hi please help me graph these polynomial inequalities. Thank you very much!
a. +25x%5E2-10x%2B1%3C0+
b. +25x%5E2-10x%2B1%3C=0+
c. +25x%5E2-10x%2B1%3E0+
d. +25x%5E2-10x%2B1%3E=0+
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
They are all based on the same parabola. Use simple logic once you have factored the quadratic and found the roots.

%285x-1%29%5E2%28versus%290, and your quadratic expression is a perfect square, so ONLY ONE ROOT OR ZERO.

The root is simple, highlight%281%29.

Now, if you know how this parabola is oriented, a quick sketch should indicate which values of x satisfy each of the inequalities you list.

(a) SO SOLUTION for this one. Strict inequality; the quadratic is non-negative everywhere. The minimum value will be 0, and you have a strict inequality for an expression stated LESS THAN ZERO.

Can you determine (b), (c), and (d) ?


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You wanted to graph them. Not sure if you want just single number line, or parabola. For example, if single number line, (d) will be the entire Real number line, or ALL x values. If parabola is what you are using, then make a SOLID curve and shade everything above and including the curve.