Problema Solution
Find a degree 3 polynomial that has zeros - 4, 3 and 7 and in which the coefficient of x^2 is -12. The polynomial is:
Answer provided by our tutors
the 3 degree polynomial with zeros x2, x2 and x3 and 'a' the coefficient of x^3
p(x)= a (x − x1) (x - x2 )(x − x3)
in our case if we put x1 = -4, x2 = 3 and x3 = 7 and a = 1 we get
p(x) = (x + 4)(x - 3)(x - 7)
p(x) = x^3 - 6*x^2 - 19x + 94
since we want the coefficient of x^2 to be -12 we multiply the above polynomial by 2
2p(x) = 2x^3 - 12*x^2 - 38x + 188
The polynomial is: 2x^3 - 12*x^2 - 38x + 188