Consider the equation 6x+15=−3(ax−b), where a and b are real numbers. which values for a and b will result in the equation having an infinite number of solutions?

For infinite number of solutions , left side should equal right side

It means the value of expression on left side must be equal to the value of expression on right side.

Now here the expression is

6x+15=−3(ax−b)

Let's first simplify this, so we get...

6x+15 = -3ax +3b

Now Comparing both sides , we can compare the terms with x and the constant terms separately

So

-3a= 6 and 3b =15

first solve for a

-3a = 6

Divide both sides by -3

a=-2

Now let's solve for b

3b=15

Divide both sides by 3

b=5,

So answer is a=-2 , b=5

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.