Question

If -4 is the zero of the polynomial x3 - x2 - 14x +24 find the other zeroes.

Answer 1

Solution is attached below

Answer 2

Answer:

Other Zeroes are 2 and 3

Step-by-step explanation:

Given: -4 is factor of x³ - x² - 14x + 24

To find: Other zeroes.

x = -4  is a zero of the polynomial then ( x + 4 ) is factor the the polynomial.

On dividing the given polynomial with factor,

Quotient = x² - 5x + 6

Division is in pic.

So,

x³ - x² - 14x + 24 = ( x + 4 ) ( x² - 5x + 6 )

                           = ( x + 4 ) ( x² - 3x - 2x + 6 )

                           = ( x + 4 ) ( x( x - 3 ) - 2( x - 3 ) )

                           = ( x + 4 )( x - 3 )( x - 2)

Now, To find zeroes,

x³ - x² - 14x + 24  = 0

( x + 4 )( x - 3 )( x - 2) = 0

x - 3 = 0      and   x - 2 = 0

x = 3   and   x = 2

Therefore, Other Zeroes are 2 and 3