![]() Let's apply this idea to our previous example: \(x^2-2x+1=0\). Tip: Make sure that the quadratic equation you are working with is written in \(ax^2+bx+c=0\) form before calculating its discriminant! To determine the number of roots a quadratic equation has, we can use a part of the quadratic formula called the discriminant: this quadratic equation only has one root). In fact, it is the only root of this equation (i.e. In our previous examples, you might have noticed that some equations had a different number of roots/solutions - 0 roots, 1 root or 2 roots.įor example, for \(x^2-2x+1=0\), we mentioned that \(x=1\) is a root/solution to this quadratic equation. So, we actually have two pairs of numbers that work in the given statement: ![]() Since \(x+y=176\), we can rearrange this equation and use it to find \(y\):Ĭhecking our work that \(y=x^2\), indeed \(163.22 \approx (12.78)^2\) Now that we our solutions, we can plug them back into the original equations to find the values for \(y\), as well as check our work to make sure our solutions are valid. Since this equation does not easily factor, we apply the Quadratic Formula to find the solutions: ![]() To determine its solutions, we need to make one side equal to 0, then factor it: Notice that we now have a quadratic equation. Now, we can substitute the first equation into the second to end up with one equation we will solve: Since "their sum is 176", we have the equation: Since we're given that "one number is the square of another", if we let \(x\) represent one number, and \(y\) represent the other number, we have the equation representing their relationship: If their sum is 176, what are the two numbers? Round answers to two decimal places. Infusion Rates for Intravenous Piggyback (IVPB) BagĮxample: One number is the square of another number.Prime Factorisation and Least Common Multiple.Learning Math Strategies (Online) Toggle Dropdown.
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