Question

Solve the equation x to the second power - 13x to the third power + 47x -35=0 given that 1 is a zero of f(x) = x to the third power-13x to the second power+ 47x-35. The solution set is?

Answer 1

The solution sets are 1, 5 and 7

Explanation:

Given the polynomial function,

f(x) = x³-13x²+47x-35

If 1 is a zero function of f(x), according to factor theorem, the linear equation x-1 is a factor of the polynomial.

To get the other solution set, we will have to divide the polynomial function by x-1 and factorize the quotient function.

Factorising the resulting quotient function.

Q(x) = x²-12x+35 = 0

= x²-5x-7x+35 = 0

= x(x-5)-7(x-5) = 0

(x-5)(x-7) = 0

x-5 = 0 and x-7 = 0

x = 5 and 7