Suppose p(x) is a polynomial of smallest possible degree such that: bullet p(x) has rational coefficients bullet p(−3)=p(sqrt7)=p(1−sqrt6)=0 bullet p(−1)=8 determine the value of p(0).

p(0) = 28.07

Step-by-step explanation:

Since p(-3)=0, it means x= -3 is a root of the polynomial. And the factor is x-(-3) = x + 3

Also, p(sqrt7)=0, meaning that x= is a root of the polynomial. And the factor is x -

Lastly, p(1-sqrt6)=0, meaning that x= is a root of the polynomial. And the factor is x -

The polynomial p(x) = K(x+3)(x-√7)(x-(1-√6))

But p(-1) = 8. That is when x = -1, p(x) = 8. So we use this to find K

K ≅ -2.44

p(0) ≅ 28.07

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step-by-step explanation: