Question

A quadratic equation is shown below: 3x2 − 15x + 20 = 0 Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points) Part B: Solve 3x2 + 5x − 8 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)

Answer 1

Answer:

$\text{The roots of }3x^2+5x-8=0\text{ are }x=1,\frac{-8}{3}$

Step-by-step explanation:

$\text{Part A: Given a quadratic equation }3x^2-15x+20=0$  

$\text{Comparing above equation with }ax^2+bx+c=0$  

a=3, b=-15, c=20

Discriminant can be calculated as

$D=b^2-4ac$

$D=(-15)^2-4(3)(20)=225-240=-15$

The roots are imaginary

The solution is

$x=\frac{-b\pm\sqrt{D}}{2a}$

$x=\frac{-(-15)\pm \sqrt{-15}}{2(3)}=\frac{15\pm\sqrt{15}i}{6}$

The roots are not real i.e these are imaginary    

$\text{Part B: Given a quadratic equation }3x^2+5x-8=0$  

$\text{Comparing above equation with }ax^2+bx+c=0$  

a=3, b=5, c=-8

Discriminant can be calculated as

$D=b^2-4ac$

$D=(5)^2-4(3)(-8)=25+96=121>0$

The roots are real

By quadratic formula method

The solution is

$x=\frac{-b\pm\sqrt{D}}{2a}$

$x=\frac{-5)\pm \sqrt{121}}{2(3)}=\frac{-5\pm 11}{6}$

$x=1,\frac{-8}{3}$

which are required roots.

I choose this method because I can get the solutions directly by substituting the values in formula, and I don't have to guess the possible solutions.