Question

Minus root 3 and root 3 are the 2 zeros of a polynomial 2x cube + x square - 6x minus 3, find the remaining 0 of it

Answer 1

the answer is this
hope this helps :)

Answer 2

Answer:

$\textbf{The remaining zero of the given polynomial is }\bf-\frac{1}{2}$

Step-by-step explanation:

Let the first zero be α = √3 and the second zero be β = -√3

The polynomial is given to be : 2x³ + x² - 6x - 3

Now, The equation containing the two zeros can be formed as :

x² + (α + β)x + α·β = 0

⇒ x² + (√3 - √3)x + √3 × -√3 = 0

⇒ x² - 3 = 0

Now, divide the given polynomial by this equation and note down the resultant quotient.

So, The quotient comes to be 2x + 1

But, since this is the equation formed by zero so this must be equal to 0

$\implies 2x + 1= 0\\\\\implies x = -\frac{1}{2}$

$\textbf{Thus, The remaining zero of the given polynomial is }\bf-\frac{1}{2}$