Question

A quadratic equation is shown below:
x2 + 5x + 4 = 0

Part A: Describe the solution(s) to the equation by just determining discriminant. Show your work. (3 points)

Part B: Solve 4x2 -12x + 5 = 0 using an appropriate method. Show the steps of your work and explain why you chose the method used. (4 points)

Part C: Solve 2x2 -10x + 3 = 0 by using a method different from the one you used in Part B. Show the steps of your work. (3 points)

Answer 1

A Quadratic Equation\[ax^2+bx+c=0\]
The Quadratic Formula\[x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]
Factored for of the Quadratic Equation\[(x-x_1)(x-x_2)=0\]

start by identifying the coefficients a,b,c

Compare
\[x^2 + 5x + 4 =0\]
With
\[ax^2+bx+c=0\]

\(a=?\) \(b=?\) \(c=?\)
______________________________

The radicand of the quadratic formula is called
the Discriminant \(\Delta =b^2-4ac\)

if \(\Delta=0\) there is only one solution to the quadratic equation
if \(\Delta>0\) there are two solutions
if \(\Delta <0\) the solutions are complex

another way of putting this
if \(\Delta=0\) there is two equal solutions
if \(\Delta>0\) there are two different solutions
if \(\Delta<0\) there are no real solutions

if \[\Delta \neq 0= d^2 \] the solutions are rational

then taking the square root in the quadratic formula will not leave any irrational component

\[x_{1,2}=\frac{-b\pm \sqrt\Delta}{2a}=\frac{-b\pm \sqrt d^2}{2a}=\frac{-b\pm d}{2a}\]