Question

please tell the answer with steps​

Answer 1

Answer:

x=-1 is the next zero

Step-by-step explanation:

STEP 1 : The given Zeroes of 3x^4 + 6x³ - 2x² - 10x - 5  are :

• √5/3 , ∴ (x - √5/3) is a factor

• -√5/3 , ∴ (x + √5/3 ) is a factor

STEP 2 :

• (x-√5/3)(x+√5/3) = x² - 5/3

• (x² - 5/3) × 3 = 3x² - 5

STEP 3 :

when 3x^4 + 6x³ - 2x² - 10 x - 5 is divided by 3x² - 5 we will get x² + 2x + 1

STEP 4 :

factorise x² + 2x + 1

x² + 2x +1 = 0

x² + x + x + 1 = 0

x(x+1) +1 (x+1) = 0

(x+1) (x+1) = 0

x = -1

∴x = -1 is a zero to the polynomial 3x^4 + 6x³ - 2x² - 10x - 5

∵Zeroes of the given polynomial are √5/3 , -√5/3 & -1.