Find a polynomial function of lowest degree with rational co

Find a polynomial function of lowest degree with rational coefficients that has the given numbers as -3, 7, 9 9, 4 + i Squareroot 8, -6 (x^3 + 4x^2 - 17x - 60)/(x + 5) Find all zeros of the Polynomial x^3 - 8x^2 + x + 42

Solution

7)-3,7,9 are roots

=>(x+3),(x-7),(x-9) are factors

=> polynomial is of the form

y =(x+3)(x-7)(x-9)

y =x³-13x²+15x+189

8)9,4+i are root

since the coefficients are reational , 4-i is also a root

(x-9),(x-(4+i)),(x-(4-i)) are factors

=> polynomial is of the form

y =(x-9)(x-(4+i))(x-(4-i))

y =(x-9)(x-4-i)(x-4+i)

y =(x-9)((x²-8x+16)+1)

y =(x-9)(x²-8x+17)

y =x³-17x²+89x -153

9)8,-6 are root

since the coefficients are reational , -8 is also a root

(x-8),(x+8),(x+6) are factors

=> polynomial is of the form

y =(x-8)*(x+8)*(x+6)

y =(x²-8)*(x+6)

y =x³+6x²-8x-48