Question

it is given that -1 is one of the zeroes of the polynomial x^3+2x^2-11x-12 find its other zeros​

Answer 1

Step-by-step explanation:

Given:-

- 1 is one of the zeroes of the polynomial x^3+2x^2-11x-12.

To find:-

Find its other zeros ?

Solution:-

Given cubic Polynomial = P(x)=x^3+2x^2-11x-12

If -1 is the zero of the polynomial ,by factor theorem ,(x+1) is the factor of P(x).

Now on dividing P(x) by (x+1) to get other zeroes

(x^3+2x^2-11x-12)/(x+1)

=>(x^3+x^2+x^2+x-12x-12)/(x+1)

=>[ (x^3+x^2)+(x^2+x)+(-12x-12)]/(x+1)

=>[ x^2(x+1)+x(x+1)-12(x+1)] /(x+1)

=>( x^2+x-12)(x+1)/(x+1)

=> x^2+x-12

=> x^2+4x-3x-12

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

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

To get zeroes we write

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

=> x+4 = 0 or x-3 = 0

=> x = -4 or x = 3

Zeroes are 3 and -4

Answer:-

The other two zeroes of the given cubic polynomial are 3 and -4

Used formula:-

Factor Theorem:-

Let P(x) be any Polynomial of the degree greater than or equal to 1 and (x-a) is another linear polynomial,if P(x)=0 then (x-a) is a factor of P(x) vice-versa.