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

`\text{The roots of }3x^2+5x-8=0\text{ are }x=1,(-8)/(3)`

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=(-b\pm√(D))/(2a)`

`x=(-(-15)\pm √(-15))/(2(3))=(15\pm√(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=(-b\pm√(D))/(2a)`

`x=(-5)\pm √(121))/(2(3))=(-5\pm 11)/(6)`

`x=1,(-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.