If m(-12) =0 is the result of M(x) using the reminder theorem then what do -12 and 0 represent?

1 answer:

3 0

Suppose we wish to determine whether or not two given polynomials with complex coefficients have a common root. Given two first-degree polynomials a0 + a1x and b0 + b1x, we seek a single value of x such that

Solving each of these equations for x we get x = -a0/a1 and x = -b0/b1 respectively, so in order for both equations to be satisfied simultaneously we must have a0/a1 = b0/b1, which can also be written as a0b1 - a1b0 = 0. Formally we can regard this system as two linear equations in the two quantities x0 and x1, and write them in matrix form as

Hence a non-trivial solution requires the vanishing of the determinant of the coefficient matrix, which again gives a0b1 - a1b0 = 0.

Now consider two polynomials of degree 2. In this case we seek a single value of x such that

Hope this helped, Hope I did not make it to complated

Please give me Brainliest

You might be interested in

The distance from one corner of a rectangular garden to the other is 13 ft. The length of the garden is 7 ft longer than the wid

coldgirl [10]

Answer:

dimensions: 12 ft by 5 ft
area: 60 ft²

Step-by-step explanation:

Let x represent the shorter dimension in feet. Then the longer one is x+7 and the Pythagorean theorem tells us the relation of these to the diagonal is ...

x² + (x+7)² = 13²

2x² +14x + 49 = 169 . . . . eliminate parentheses

x² +7x -60 = 0 . . . . . subtract 169 and divide by 2

(x +12)(x -5) = 0 . . . . factor the equation

x = -12 or +5 . . . . . . . only the positive value of x is useful here.

The short dimension is 5 ft, so the long dimension is 12 ft. The area is their product, 60 ft².

_____

<em>Comment on finding the area</em>

The quadratic equation above can be rearranged and factored as ...

x(x +7) = 60

Since the dimensions of the garden are x and (x+7), this product is the garden's area. This equation tells us the area is 60. We don't actually have to find the dimensions.

4 0

3 years ago

092:15 PMEach month, henry weeds gardens for 15 hours and mows lawns for x hours.For each job, he is paid $9 per hour. He wants

ankoles [38]

We know that he weeds gardens for 15 hours, and mows lawns for x hours.

If he wants to earn $252 per month, we can express the following

$9\cdot15+9x\ge252$

Now, we solve for x

$\begin{gathered} 135+9x\ge252 \\ 9x\ge252-135 \\ 9x\ge117 \\ x\ge\frac{117}{9} \\ x\ge13 \end{gathered}$ <h2>Hence, he has to mow lawns for 13 hours to earn at least $252.</h2>