Question

if 1 and -2 are two zeroes of x³ - 4x² - 7x + 10, find its third zero.​

Answer 1

Answer:  

Given : 1 and −2 are the zeros of the given polynomial therefore (x−1) and (x+2) are factors of f(x)

Consequently ,(x−1)(x+2)=(x  

2

+x−2) is a factor of f(x)  

Divide x  

3

−4x  

2

−7x+10 by (x  

2

+x−2)

put f(x)=0

(x  

2

+x−2)(x−5)=0

(x−1)(x+2)(x−5)=0

x=1  or x=−2 or x=5

hence , the third zero is 5.

Step-by-step explanation:

Answer 2

Answer:

(x+2) is a factor of f(x). Consequently, (x–1) (x+2) = (x^2 + x – 2) is a factor of f(x). Hence, the third zero is 5.