Question

quadratic polynomial 2x^2-3x+1 has zeros as alpha and beta find the quadratic polynomial whose zeros are 3 alpha and 3 beta?

Answer 1

Solution :

The given polynomial is

f(x) = 2x² - 3x + 1

Since α and β are the zeroes of f(x),

• α + β = - (- 3)/2 = 3/2
• αβ = 1/2

We have to find the polynomial whose zeroes are 3α and 3β, which can be found as

g(x) = (x - 3α) (x - 3β)

= x² - 3αx - 3βx + 9αβ

= x² - 3 (α + β) x + 9αβ

= x² - 3 (3/2) x + 9 (1/2)

= x² - 9x/2 + 9/2

= (2x² - 9x + 9)/2

i.e., 2x² - 9x + 9