Question

Find all the zeroes of the polynomial p(x) =3x^4+6x^3-2x^2-10x-5​

Answer 1

Answer:

{- 1, - 1.291, 1.291}

Step-by-step explanation:

I would check (- 1) first.

3(-1)^4 + 6(-1)^3 - 2(-1)^2 - 10(-1) - 5 = 3 - 6 - 2 + 10 - 5 = 0

$x_{1}$ = - 1 is a zero of given polynomial.

(3x^4 + 6x^3 - 2x^2 - 10x - 5) ÷ (x + 1) = 3x³ + 3x² - 5x - 5

3x³ + 3x² - 5x - 5 = 3x²(x + 1) - 5(x + 1) = (x + 1)(3x² - 5)

If (x + 1)(3x² - 5) = 0, then

$x_{2}$ = - 1  

3x² - 5 = 0 ⇒ x² = $\frac{5}{3}$

$x_{34}$ = ± $\sqrt{5/3}$ ≈ ± 1.291

{-1, - 1.291, 1.291}