Question

Follow the Steps to Make the Formula Valuable! Instruction: Find the solutions of each of the following quadratic equations using the quadratic formula. Then, fill in the table by supplying the missing task and answer the questions that follow. 1. 2x² +9x== STEPS TASK b, a. Write the equation in standard form b. Determine the values of a, and c. c. Substitute the values of a, b, and e in the quadratic formula. d. Simplify the result. e. Value/s of the variable. 2. 3(x-4)2+11-0 STEPS TASK a. Write the equation in standard form. b. Determine the values of a, b, and c. c. Substitute the values of a, b, and e in the quadratic formula d. Simplify the result. e. Value/s of the variable. Guide Questions: a. How did you use the quadratic formula in finding the solution/s of each equation? b. How many solutions does cach equation have?​

Answer 1

Step-by-step explanation:

⟨1.⟩

Given equation is 2x²+9x = -4

⇛ 2x²+9x+4 = 0

The standard form of the equation is 2x²+9x+4 = 0

On comparing the given equation with ax²+bx+c = 0

We have

a = 2

a = 9

c = 4

By using Quadratic Formula

x = [-b±√(b²-4ac)]/2a

On Substituting these values in the above formula then

⇛ x = [-9±√{9²-4(2)(4)}]/2(2)

⇛ x = {-9±√(81-32)}/4

⇛ x = {-9±√49}/4

⇛ x = (-9±7)/4

⇛ x = (-9+7)/4 or (-9-7)/4

⇛ x = -2/4 or -16/4

⇛ x = -1/2 or -4

The roots are -1/2 and -4

⟨2.⟩

Given equation is 3(x-4)²+11 = 0

⇛ 3(x²-8x+16)+11 = 0

⇛ 3x²-24x+48+11 = 0

⇛ 3x²-24x+59 = 0

The standard form of the equation is

3x²-24x+59= 0

On comparing the given equation with ax²+bx+c = 0

We have

a = 3

= 3b = -24

= 3b = -24c = 59

By using Quadratic Formula

x = [-b±√(b²-4ac)]/2a

On Substituting these values in the above formula then

⇛ x = [-(-24)±√{(-24)²-4(3)(59)}]/2(3)

⇛ x = {24±√(576-708)}/6

⇛ x = {24±√-132}/6

⇛ x = {24±2(-33)}/6

⇛ x = 2(12±√-33)/6

⇛ x = (12±√-33)/3

The roots are (12+√-33)/3 and

(12-√-33)/3

⟨a.⟩

I used the Quadratic Formula bu substituting the values of a , b and c values in it.

⟨b.⟩

Given two equations are Quadratic equations so they have two solutions or roots.

Since the degree of the Quadratic equations is 2.

Hope this helps!!

If you have any doubt, then you can ask me in the comments.