Question

If the zeros of the polynomial f(x)=x²-px + 12 are of the form a-b, a+b, then find all the zeros.​

Answer 1

let 2 zeroes be a and b of polynomial x

+px +q=0

sum of roots = a +b=-p/1=-p

products of roots = ab = q/1= q

(a+b? a2 + b2 + 2ab a +b = p?-2q

(a-b)* = as +b5-2ab = p-2q-2q =p

4q

now ques asks for new quadratic eq

whose roots are (a+b) and (a-b)

so sum of new roots are = (a +b) + (a-b)

Fptp-4q = 2p- 4q

and product of roots = (a+b)"(a-b)* =

(P1 (ps-4q)* = p" (p* +16q5 + 8pfq)

hence new quadratic eq gonna be

x- x(sum of roots) + (products of roots)

x- x(2p- 4q) + p°(p* + 16q +8pq) = 0