Question

If √5 and-√5are the two zeroes of the polynomial. x^3+3 x^2-5 x-15,find its third zero.​

Answer 1

Answer:

given cubic polynomial = x³ + 3x² -5x - 15

here,

a = 1

b = 3

c = - 5

d = -. 15

given, that √5 and -√5 are the zeroes,

let the other zero be ß

sum of zeroes = -b/a

=> => - √5 + √5 + ß = -3/1

=> ß = - 3

so the other zero is - 3

Answer 2

use the identity

a2-b2 =(a+b) (a-b)

so , (x-root5 ) (x+root5) = x^2-5

so we have the factor of x^3+3x^2-5x+15 isx^2-5

so, we need to divide the whole p(x) by x^2-5

we find the quadratic polynomial so that polynomial you have to middle splitting terms

and hence you find zeroes ok