Question

If-1 is a zero of the polynomial f(x) = x2 - 7x-8, then the other zero is
a) 6
b) 8
c)-8​

Answer 1

Answer:

b

Step-by-step explanation:

by hit and trial method 8 is the other zero .

x2-7x-8

x=8

therefore ,

8^2-7×8_8

64-56-8

64-64=0

Answer 2

★ Given :

-1 is a zero of polynomial f(x) = x² - 7x - 8

★ To find :

The other zero

”★ Solution :

-1 is a zero of f(x) , then (x+1) is a factor of x² - 7x - 8 by factor theorem .

other factor of x² - 7x - 8 =

$\dfrac{x^2 - 7x - 8}{x+1}$

x² - 7x - 8

by middle term splitting

= x² -8x + x - 8

= x(x+1) -8(x +1)

= (x-8) (x+1)

$= \dfrac{(x - 8) \cancel{(x+1)}}{\cancel{(x+1)}}$

★ Therefore , other factor of f(x) = (x-8) ..

_______________________________________

x - 8 = 0

x = 8

→ therefore , the other zero of f(x) = x² - 7x - 8 is 8 by factor theorem. (option b)

★ Additional Information -:

$\purple{Remainder \: theorem}$ - The remainder theorem states that when a polynomial, f(x), is divided by a linear polynomial , x - a, the remainder of that division will be equivalent to f(a).