8.1 FE Review - Mathematics#
Readings#
Videos#
Example 3#
Select all the root(s) in \(f(x)=x^2−4x−3\).
A. \(4+\sqrt{3}\)
B. \(2+\sqrt{7}\)
C. \(2−\sqrt{7}\)
D. \(4−\sqrt{3}\)
Work it out#
To find the roots of an equation, first set \(f(x)\) to 0.
\(x^2−4x−3=0\)
For simple equations, you can factor them by hand, but this equation does not factor easily. 3 can be factored into 1 and 3. However, one must be negative and one positive for their multiple to be -3. There is no way to sum those to get -4. Instead simply use the quadratic formula (a.k.a. the quadratic equation) if the equation can’t be factored easily or if you are unsure. A quadratic equation is of the form:
\(ax^2+bx+c=0\)
So we have \(a=1\), \(b=−4\), and \(c=−3\). The quadratic formula is:
\(x= \frac{-b \pm \sqrt{b^2-4ac}}{2a}\)
Substitute and solve as
\(x= \frac{-(-4) \pm \sqrt{(-4)^2-4(1)(-3)}}{2(1)} = 2 \pm \sqrt{7}\)
Choose B and C