Question

Obtain all other zeros of P(x) =(x⁴+2x³-27x²-6x+72 ) two zeros are √3 and √-3​

Answer 1

Answer:

All the zeroes of the polynomial are root 3, -root 3 , +4 and -6

Explanation:

Since root 3 and -root 3 are zeroes of the polynomial,

(x + root 3) and (x - root 3) are factors of the polynomial.

Therefore,

Dividing, P(x) with (x + root 3)(x - root 3) ,i.e, (x^2 - 3), we will get the other two factors,

On dividing we get the remainder as zero and the quotient as (x^2 + 2x - 24)

x^2 + 2x - 24 = (x - 4)(x + 6)

Therefore,

The other two zeroes are 4 and -6.