Question

If 2 zeros of the polynomial x⁴- 6x³-26x²+138-35 are 2+√3 and 2-√3,find other zeros.​

Answer 1

Answer:

since 2+√3 is zero

x-(2+√3) is a factor of polynomial

since 2-√3 is a zero

x-(2-√3) is a factor of polynomial

this means (x-2-√3)(x-2+√3)

(x-2)^2-(√3)^2

x^2-4x+4-3

x^2-4x+1

x^2-4x+1 is a factor of x^4-6x^3-26x^2+138x-35

so we divide them with algorithm method

we get answer x^2-2x-35

x^2-7x+5x-35

X(x-7)+5(x-7)

(X+5)(x-7)

The other zeroes are

-5and 7