Question

if alpha amd beta are zeroes of the quadrqtic formula 2x^2-3+5x,then find the quadratic polynomial whose zeroes are (alpha+2×beta) and (2×alpha+beta)

Answer 1

Answer:

x² + 15/2 x + 53/3

Step-by-step explanation:

α + β = -b/a = -5/2 αβ = c/a= -3/2

α + 2β and 2α + β

α + 2β + 2α + β = 3 α + 3 β = 3 ( α + β )= -15/2

α + 2β x 2α + β = 2 α² + αβ + 4 αβ + 2 β²

= -3/2 - 6 + 2 ( α² + β² )

= -3-12/6 + 2{ ( α + β )² - 2 αβ }

= -15/2 + 37/2

=11

Polynomial = x² - ( α + β ) x + αβ

= x² + 15/2 x + 11 or 2x² + 15 x  + 22