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Describe the solution(s) to 9x² - 36x + 36 = 0 by just determining the radicand. Show your work. (10 points) Part B: Describe the solution (s) to x²-x + 4 = 0 by just determining the radicand. Show your work. (10) points) Part C: Solve 4x² + 23 – 35 using an - appropriate method. Show the steps of your work and explain why you chose the method used​

Sagot :

MrRoyal

The solution to the equations are:

  • 9x² - 36x + 36 = 0 has two equal real solutions
  • x² - x + 4 = 0 has no real solutions
  • The factored expression of 4x² + 23 – 35 is 4(x² -3)

Part A: Describe the solution

The equation is given as:

[tex]9x\² - 36x + 36 = 0[/tex]

The above equation is a quadratic equation which can be represented as:

[tex]ax\² + bx + c = 0[/tex]

The discriminant (d) is calculated as:

[tex]d = b\² - 4ac[/tex]

So, we have:

[tex]d = (-36)\² - 4 * 9 * 36[/tex]

[tex]d = 0[/tex]

A discriminant of 0 means that the equation has two equal real solutions

Hence, 9x² - 36x + 36 = 0 has two equal real solutions

Part B: Describe the solution

The equation is given as:

[tex]x\² - x + 4 = 0[/tex]

The above equation can be represented as:

[tex]ax\² + bx + c = 0[/tex]

The discriminant (d) is calculated as:

[tex]d = b\² - 4ac[/tex]

So, we have:

[tex]d = (-1)\² - 4 * 1 * 4[/tex]

[tex]d = -15[/tex]

A discriminant of -15 means that the equation has no real solutions

Hence, x² - x + 4 = 0 has no real solutions

Part C: The solution to the expression

We have:

[tex]4x\² + 23 - 35[/tex]

Evaluate the difference

[tex]4x\² -12[/tex]

Factor out 4

[tex]4(x\² -3)[/tex]

Hence, the factored expression of 4x² + 23 – 35 is 4(x² -3)

Read more about quadratic expressions at:

brainly.com/question/10449635

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