The least degree polynomial function with integral coefficients and the given zeros, -1, 3+3i is f(x) = x³ + x².
What do we mean by polynomial function?
- A polynomial function is one that involves only non-negative integer powers or positive integer exponents of a variable in an equation such as the quadratic equation, cubic equation, and so on.
- For example, 2x+5 is a polynomial with an exponent of one.
So, given zeroes are -1, 3+3i.
- We got: x = -1
- Then, x + 1 = 0.
- Hence, one factor of the polynomial function is (x+1).
Similarly,
- We have: 3+3i
- Rewrite as: x = 3 + √-9
- Square both the sides: x² = 9 - 9
- So, the other factor is x².
So, the polynomial has the function: (x+1)x²
- (x+1)x²
- x³ + x²
- f(x) = x³ + x²
Therefore, the least degree polynomial function with integral coefficients and the given zeros, -1, 3+3i is f(x) = x³ + x².
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