Question

If alpha and beta are the zeros of the quadratic polynomial x2-1 find a quad poly 2 alpha/beta and beta/alpha

Answer 1

Answer:

The required quadratic polynomial is x² + 3x + 2.

Step-by-step-explanation:

The given quadratic polynomial is x² - 1.

To find the zeros of quadratic polynomial, we equate it to zero.

∴ x² - 1 = 0

⇒ x² = 1

⇒ x = ± √1

⇒ x = ± 1

Let α = 1 and β = - 1.

Now, the given zeros are 2α / β and β / α.

2α / β = 2 * 1 / - 1

⇒ 2α / β = 2 / - 1

⇒ 2α / β = - 2

And,

β / α = - 1 / 1

⇒ β / α = - 1

Now, the quadratic polynomial is in the form

P ( x ) = x² - ( Sum of zeros ) x + ( Product of zeros )

⇒ P ( x ) = x² - [ ( 2α / β ) + ( β / α ) ] x + [ ( 2α / β ) * ( β / α ) ]

⇒ P ( x ) = x² - ( - 2 - 1 ) x + [ - 2 * ( - 1 ) ]

⇒ P ( x ) = x² - ( - 3 ) x + ( 2 )

⇒ P ( x ) = x² + 3x + 2

∴ The required quadratic polynomial is x² + 3x + 2.