Question

Which quadratic function has a bigger positive solution?

f(x)=2x^2-32 g(x)=12x^2-48 h(x)=100x^2

Explain your answer.

Answer 1

h(x)=100x^2

Hope this helped :D

Simplifying

x = 100x2

Solving

x = 100x2

Solving for variable 'x'.

Combine like terms: 100x2 + -100x2 = 0

x + -100x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.

x(1 + -100x) = 0

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve:

Simplifying

x = 0

Solving

x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying

x = 0

Subproblem 2

Set the factor '(1 + -100x)' equal to zero and attempt to solve:

Simplifying

1 + -100x = 0

Solving

1 + -100x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.

1 + -1 + -100x = 0 + -1

Combine like terms: 1 + -1 = 0

0 + -100x = 0 + -1

-100x = 0 + -1

Combine like terms: 0 + -1 = -1

-100x = -1

Divide each side by '-100'.

x = 0.01

Simplifying

x = 0.01

Solution

x = {0, 0.01}Simplifying

x = 100x2

Solving

x = 100x2

Solving for variable 'x'.

Combine like terms: 100x2 + -100x2 = 0

x + -100x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.

x(1 + -100x) = 0

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve:

Simplifying

x = 0

Solving

x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying

x = 0

Subproblem 2

Set the factor '(1 + -100x)' equal to zero and attempt to solve:

Simplifying

1 + -100x = 0

Solving

1 + -100x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.

1 + -1 + -100x = 0 + -1

Combine like terms: 1 + -1 = 0

0 + -100x = 0 + -1

-100x = 0 + -1

Combine like terms: 0 + -1 = -1

-100x = -1

Divide each side by '-100'.

x = 0.01

Simplifying

x = 0.01

Solution

x = {0, 0.01}

Answer 2

Hello from MrBillDoesMath!

Answer:

f(x) has the largest positive solution.

Discussion:

f(x) = 2x^2 - 32 = 2(x^2-16) = 2(x-4)(x+4)

g(x) = 12x^2 - 48 = 12 (x^2-4) = 12 (x+2)(x-2)

h(x) = 100x^2 only has x = 0 as a solution (i.e. it does not have a positive root)

The root x = 4 of f(x) is larger than the root x = 2 of g(x).

Thank you,

MrB