Question

A quadratic equation is shown below:

6x2 + 17x + 9 = 0

Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points)

Part B: Solve 4x2 − 4x + 1 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)

(10 points)

Answer 1

x = -0.70,-2.212.

Explanation:

(a) The quadratic equation is :

`6x^2 + 17x + 9 = 0`

Here,

a = 6, b = 17, c = 9

Put all the values in the quadratic formula.

`x=(-17+√(17^2-4* 6* 9))/(2(6)),(-17-√(17^2-4* 6* 9))/(2(6))\\\\x=-0.70,-2.12`

So, the solution of the given equation are -0.70,-2.212.

(b) Equation is :
`4x^2 -4x + 1 = 0`.

Here, a = 4, b = -4 and c = 1

So,

`x=(-(-4)+√((-4)^2-4* 4* 1))/(2(4)),(-(-4)-√((-4)^2-4* 4* 1))/(2(4))\\\\x=0.5,0.5`

Hence, this is the required solution.