Find the x-intercept(s) of f(x)=3x^4−30x^3+75x^2
enter intercept(s) as points

(0, 0) and (5, 0)

Step-by-step explanation:

f(x) = 3x⁴−30x³+75x²

(a) Factor the polynomial

3x⁴−30x³+75x² = 3x²(x² -10² + 25)

                        = 3x²(x - 5)²

(b) Solve the polynomial

3x²(x - 5)² = 0

x² = 0     x - 5 = 0

x  = 0           x = 5

The x-intercepts are at (0, 0) and (5, 0).

The Figure below shows the graph of your polynomial with the x-intercepts at (0, 0) and (5, 0).

(-3, -129)

Step-by-step explanation:

Given

Two lines:

are perpendicular to each other and intersect at point (-8,3).

To find: (P, Q)

Solution:

The two lines intersect at (-8,3).

It means, the equation of line will be satisfied when we put value of x = -8 and y = 3

Putting in the second equation, we will get an equation in P and Q:

Given that two lines are perpendicular.

It means the product of their slopes will be equal to -1.

i.e.

Slope of a line of the form is given as:

So, slopes of given lines are:

Using the condition:

Putting the value of P in equation (1):

So, answer is (-3, -129)