Answer:
The needed quadratic equation is : [tex]p(x) = x^2 -3x + 10[/tex]
Step-by-step explanation:
The given equation is of the form [tex]p(x) = ax^2 + bx + c[/tex]
The given solutions of the equations are:
x = 3 +i, x = 3 - i
Now, if x = a is the zero of the polynomial p(x)
⇒(x -a ) is the root of the given polynomial.
⇒ (x - ( 3+i)) and (x - ( 3+i)) are the given roots for p(x)
P(X) = PRODUCT OF ALL ROOTS
⇒ p(x) = (x - ( 3+i))(x - ( 3-i)) = ( x-3 -i)(x -3+i)
Now, [tex](a-b)(a +b) = a^2 - b^2\\\implies ( (x-3)-i)((x-3)+i) = (x-3)^2 - (i)^2 = x^2 +9 - 3x -(-1)\\= x^2 +10 - 3x\\\implies p(x) = x^2- 3x + 10[/tex]
Hence, the needed quadratic equation is : [tex]p(x) = x^2 -3x + 10[/tex]
