Question

The drop down menus choices are: two imaginary solutionstwo real solutionsone real solution

Answer 1

Given a quadratic equation of the form:

`ax^2+bx+c=0`

The discriminant is:

`D=b^2-4ac`

And we can know the number of solutions with the value of the discriminant:

• If D < 0, the equation has 2 imaginary solutions.

,

• If D = 0, the equation has 1 real solution

,

• If D > 0, the equation has 2 real solutions.

Equation One:

`x^2-4x+4=0`

Then, we calculate the discriminant:

`D=(-4)^2^-4\cdot1\cdot4=16-16=0`

D = 0

There are 1 real solution.

Equation Two:

`-5x^2+8x-9=0`

Calculate the discriminant:

`D=8^2-4\cdot(-5)\cdot(-9)=64-20\cdot9=64-180=-116`

D = -116

There are 2 imaginary solutions.

Equation Three:

`7x^2+4x-3=0`

Calculate the discriminant:

`D=4^2-4\cdot7\cdot(-3)=16+28\cdot3=16+84=100`

D = 100

There are 2 real solutions.

Answers:

Equation 1: D = 0, One real solution.

Equation 2: D = -116, Two imaginary solutions.

Equation 3: D = 100, Two real solutions.