Question

-root3 are the two zeros of a polynomial
2x minus root 3 and root 3 are the two zeros of the polynomial 2 x cube + x square - 6 x minus 3 find the remaining zero of it

Answer 1

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Answer 2

Answer:

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

Step-by-step explanation:

Let the first zero be a = √3

and the second zero be b = -√3

Given that the equation of the polynomial is : 2x³ + x² - 6x - 3

Using the given two zeros the new equation could be formed as :

x² + (a + b)x + a·b = 0

⇒ x² + (√3 - √3)x + √3 × -√3 = 0

⇒ x² - 3 = 0

Now, if we divide the polynomial equation with the above equation, the quotient comes to be 2x + 1

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

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

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