Form a Polynomial Function Transfer Task - Algebra 2?
A polynomial function with integer coefficients has zeroes of -3, 1/2, and 1+i . Write the function in standard form.
(please explain work)
A polynomial function with integer coefficients has zeroes of -3, 1/2, and 1+i . Write the function in standard form.
(please explain work)
?
Favorite Answer
p(x) = (x+3)(2x-1)(x-1-i)... this will have some complex coefficients. We avoid this by including the complex conjugate of 1+i as a zero.
p(x) = (x+3)(2x-1)(x-1-i)(x-1+i)
p(x) = (2x²-x+6x-3)(x²+(-1+i + -1-i)x+(-1-i)(-1+i))
p(x) = (2x²+5x-3)(x²-2x+2)
p(x) = 2x⁴ + (5-4)x³ + (-3-10+4)x² + (10+6)x - 6
p(x) = 2x⁴ + x³ - 9x² + 16x - 6 is a polynomial function with integer coefficients that has zeroes of -3, 1/2, and 1+i.