Probably the easiest way to do this is to use synthetic division. We already know one of the zeros of the quadratic so we can use that number to find the other zero. If the point is (4, 0), then when y = 0, x = 4. Thus, 4 is a zero. Put 4 outside the "box" and put the coefficients from the quadratic inside, like this: 4 (1 -1 -12). Draw a line and bring down the first one under it. Multiply that 1 by the 4 to get 4. Put that 4 up under the -1 and add to get 3. Multiply 3 by 4 to get 12. Put that 12 up under the -12 and add to get 0. The numbers left under the line are the coefficients for the next polynomial, called the depressed polynomial, and this polyomial is one degree less than the one we started with. Those coefficients are 1 and 3. Therefore, the polynomial is x + 3 = 0. That means that the other zero, or x-intercept, is x = -3.

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3 years ago

Express the situation as a system of two equations in two variables. Be sure to state clearly the meaning of your x- and y-varia

expeople1 [14]

Answer:

9 TV ads and 20 radio ads

Step-by-step explanation:

He has $37,000 to spend. He has to sum that amount of money between the TV and radio ads. Each TV ad costs $3000 while each radio ad costs $500, so the equation that represents that is 37000 = 3000x + 500y

The same happens with the amount of voters he needs to reach, the equation is 130000 = 10000x + 2000y

The system that represents this is

$\left \{ {{3000x+500y=37000} \atop {10000x+2000y=130000}} \right.$