In 9x^2-2x+10, the discriminant is (-2)^2-4*9*10=(4-360)=-356, is negative and not the square of a rational number. Hence we cannot factorize it by splitting middle term.
Hence, the way is to find out zeros of quadratic trinomial 9x^2-2x+10. Zeros of ax^2+bx+c are given by quadratic formula (-b+-sqrt(b^2-4ac))/(2a).
So its zeros, which are two complex conjugate numbers are given by quadratic formula and are
(-(-2)+-sqrt(-356))/(2xx9) or
(2+-2sqrt89i)/18 or
(1+-sqrt89i)/9 i.e. (1-sqrt89i)/9 and (1+sqrt89i)/9
Now, if alpha and beta are zeros of quadratic polynomial, then its factors are (x-alpha)(x-beta). However as we have 9 as coefficient of x^2, we should multiply it by 9
Hence factors of 9x^2-2x+10 are 9(x-(1+isqrt89)/9)(x-(1-isqrt89)/9).
