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One particular solution is x = 0, y = 0, z = 0. Two other solutions are x = 3, y = 6, z = 1, and x = 8, y = 9, z = 2. There is a unique plane in three-dimensional space which passes through the three points with these coordinates, and this plane is the set of all points whose coordinates are solutions of the equation.
The roots of the quadratic function y = 1 / 2 x 2 − 3x + 5 / 2 are the places where the graph intersects the x-axis, the values x = 1 and x = 5. They can be found via the quadratic formula. In elementary algebra, the quadratic formula is a closed-form expression describing the solutions of a quadratic equation.
The simplified equation is not entirely equivalent to the original. For when we substitute y = 0 and z = 0 in the last equation, both sides simplify to 0, so we get 0 = 0, a mathematical truth. But the same substitution applied to the original equation results in x/6 + 0/0 = 1, which is mathematically meaningless.
If the original fact were stated as "ab = 0 implies a = 0 or b = 0", then when saying "consider abc = 0," we would have a conflict of terms when substituting. Yet the above logic is still valid to show that if abc = 0 then a = 0 or b = 0 or c = 0 if, instead of letting a = a and b = bc , one substitutes a for a and b for bc (and with bc = 0 ...
The solutions of the quadratic equation ax 2 + bx + c = 0 correspond to the roots of the function f(x) = ax 2 + bx + c, since they are the values of x for which f(x) = 0. If a , b , and c are real numbers and the domain of f is the set of real numbers, then the roots of f are exactly the x - coordinates of the points where the graph touches the ...
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The Walter Payton Man of the Year award will be presented during the annual NFL Honors show on CBS on Feb. 8 at 9 p.m. ET. This article originally appeared on USA TODAY: Walter Payton NFL Man of ...
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