Question

The equation 3x2 = 6x – 9 has two real solutions
True
O False

Answer 1

Answer: FALSE

Explanation:

Rewrite the given equation in the form
`ax^2+bx+c=0`, then:

`3x^2 = 6x - 9\\3x^2-6x +9=0`

Now, we need to calculate the Discriminant with this formula:

`D=b^2-4ac`

We can identify that:

`a=3\\b=-6\\c=9`

Then, we only need to substitute these values into the formula:

`D=(-6)^2-4(3)(9)`

`D=-72`

Since
`D<0` the equation has no real solutions.

Answer 2

False

Explanation:

We first write the equation in the form ax² + bx + c=0 which gives us:

3x² - 6x + 9=0

Given the quadratic formula,

x= [-b ±√(b²- 4ac)]/2a ,the discriminant proves whether the equation has real roots or not.

The discriminant, which is the value under the root sign, may either be positive, negative or zero.

Positive discriminant- the equation has two real roots

Negative discriminant- the equation has no real roots

Zero discriminant - The equation has two repeated roots.

In the provided equation, b²-4ac results into:

(-6)²- (4×3×9)

=36-108

= -72

The result is negative therefore the equation has no real solutions.