Question

Quadratic polynomial 2x³ - 3x² + 1 has zeroes as α and β. Now, form a quadratic polynomial whose zeroes are 3α and 3β

Answer 1

Answer:

α+β= - coefficient of x /coefficient of x²

α+β=3/2   ---(1)

αβ= constant /coefficient of x²

αβ=1/2   ----(2)

Now,

sum of zeroes=3α + 3β

=3(α+β)

=3 x 3/2        (from (1))

=9/2     ----(*)

and,

product of zeroes= 3α x 3β

=9 x αβ

=9 x 1/2        (from (2))

=9/2     ----(**)

Now,

quadratic equation is

⇒x² - (sum of roots)x + product of zeroes=0

⇒x² - (9/2)x + 9/2 =0                (from (*) and (**))

⇒x²-9/2x +9/2 =0

⇒2x²- 9x +9 =0          (Answer)

Hope this will help you...