Write a polynomial function of least degree and leading coefficient 1 that has the given roots.
1. 3, 2 + √6

2. 4, 7i

3. √11, 1/4

To find to polynomial from zeros.

Find the factors. If it is a positive zero, the factor will be (x- zero) If it is a negative zero if is (x+zero)

Multiply the factors together.

Zeros of -4, -2, 5 would be:

Find the factors: (x+4)(x+2)(x-5)

Multiply the factors together: Will start out with FOIL for (x+4)(x+2) = x2+2x+4x+8 Combine like terms. Then multiply by the last factor

(x2+6x+8)(x-5) using the distributive property

x3+6x2+8x-5x2-30x-40 Combine like terms

x3+x2-22x-40

For the next one, the factors are a bit more complicated because of the radical. With a radical, you will also have to have a factor with the conjugate (Same term opposite sign)

4, 6, negative square root of 7

Factors would be: (x-4)(x-6)(x-√7)(x+√7) You can FOIL the first 2 factors and the last 2, then multiply them together using the distributive property.

distance covered by pamela in 9 l of fuel = 99km

let us apply unitary method here.

distance covered by pamela in 1 l of fuel =99/9 =11 km

now let us find distance covered by pamela if she has 12 l of fuel.

distance covered in 12 l = distance covered in 1 l of fuel * 12

we know that distance covered by here in 1 l is 11 km.

so distance covered in 12 l of fuel = 11*12 = 132 km.