Find a degree polynomial that has zeros -3,4 and 5 and in which the coefficient of x^2 is 12.
2 2/3 +1 1 1/3 /6 2/5
2x
(-4x+2)(x+5)
To find a degree polynomial with given zeros and a specific coefficient of x^2, we will use the fact that if a polynomial has a zero at x = a, then it has a factor of (x - a).
In this case, the zeros are -3, 4, and 5. Therefore, the polynomial will have factors of (x + 3), (x - 4), and (x - 5).
To find the polynomial, we need to multiply these factors together and multiply the result by a constant to get the coefficient of x^2.
So, the polynomial will be:
P(x) = c(x + 3)(x - 4)(x - 5)
To find the value of the constant 'c', we use the fact that the coefficient of x^2 is 12.
Expand the polynomial:
P(x) = c(x^2 - x - 12)(x - 5)
Now, compare the coefficient of x^2 in the expanded polynomial with the given coefficient of 12.
Coefficient of x^2 = c * 1 * 1 = c
We know that the coefficient of x^2 is 12, so:
c = 12
Substituting this value back into the polynomial, we get:
P(x) = 12(x^2 - x - 12)(x - 5)
Therefore, the degree polynomial with zeros -3, 4, and 5 and a coefficient of x^2 as 12 is:
P(x) = 12(x^2 - x - 12)(x - 5)