Find the rational zeros and then other zeros of the polynomial function f(x)=x3 − 17x2 + 55x + 25, that is, solve f(x)=0 Factor f(x) into linear factors

Question

Find the rational zeros and then other zeros of the polynomial function f(x)=x3 − 17x2 + 55x + 25,  that is, solve f(x)=0  Factor f(x) into linear factors

cyhuddwyr9 · Accepted Answer

To find the rational zero and other zeros of the polynomial f(x)=x3 − 17x2 + 55x + 25 Factor f(x) into linear factors Let us solve the equation. f(x)=0 x3 − 17x2 + 55x + 25=0 ∵ the constant term has factors 1 and 5. Let us whether these can be zeros. f(1)=1 − 17 + 55 + 25=64 ≠ 0 ∴ x=1 can not be zero of f(x). f(5)=53 − 17(5)2 + 55(5) + 25=125 − 425 + 275 + 25= −300 + 300=0 ∴ x=5 is a rational zero of f(x). We can write, f(x)=x2(x − 5) −12x(x − 5) − 5(x − 5) =(x − 5)(x2 − 12x − 5) Now we only need to solve the quadratic equation. x2 − 12x − 5=0 Then x=−(−12) ± (−12)2 4(1)(−5)2(1) =12 ± 144 + 202 =12 ± 1642 =12 ± 2412 =6 ± 41 Therefore, there is only one rational zero, 5 and other zeros are 6 + 41, 6 − 41 The factorization of f(x), f(x)=(x − 5)(x − (6 − 41))(x − (6 + 41)) =(x − 5)(x − 6 + 41)(x − 6 − 41)

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

Find the rational zeros and then other zeros of the polynomial function f(x) = x^{3} - 17x^{2} + 55x + 25, that is, solve f(x) = 0 Factor f(x) into linear factors

Answered question

Answer & Explanation

New Questions in Algebra II