Because they know they are about to take the square root and will want to bring the two outside of it. They are being overly descriptive.Nathi ORea said:
They are probably assuming that you already know this (i.e., there is not a section coming) so you will probably want to review this on your own.Nathi ORea said:
Typo in your work. The above should be ##16 - 4(3)(-1) = 28##.Nathi ORea said:
You've been a member here for almost three years. Please take the time to learn at least the rudiments of how to write mathematical expressions. At the very least, b^2 - 4ac. Better yet, using LaTeX to write ##b^2 - 4ac##. When you're creating a post, there's a link to our LaTeX tutorial in the lower left corner.Nathi ORea said:
It's a convention to take any square factors out of a square root. For example, if you ended up with ##\sqrt 4##, that wouldn't be wrong in itself. But, the convention is to write that as ##\sqrt 4 = 2##.Nathi ORea said:
Ahhhh.. so that’s why they did it! Thank you very muchPeroK said:
If one is looking for a numeric result, ie, a decimal answer (such as the 0.215 quoted in the OP), today you simply punch "SQRT 28" into your hand calculator and move on. That's actually fewer keys pressed than "2 times SQRT 7". In the old days, I think algebra lessons stopped at ##2\sqrt 7##. Maybe because evaluating ##\sqrt 7## was an exercise in table lookups, or log tables, or slide rules; and these were topics/skills mastered prior to algebra.PeroK said:
Quadratic equations are used to model many real-life situations, such as projectile motion, population growth, and financial analysis. Understanding them allows us to make predictions and solve problems in various fields of science and engineering.
The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. This form is also known as the standard form.
There are several methods for solving quadratic equations, including factoring, completing the square, and using the quadratic formula. The method you choose depends on the specific equation and your personal preferences.
The discriminant is the part of the quadratic formula under the square root sign, b^2 - 4ac. It tells us the nature of the solutions to the equation. If the discriminant is positive, the equation has two distinct real solutions. If it is zero, there is one real solution. And if it is negative, there are no real solutions.
Yes, quadratic equations can have imaginary solutions when the discriminant is negative. In this case, the solutions are complex numbers in the form a + bi, where a and b are real numbers and i is the imaginary unit (i = √-1).