If alpha and beta are the zeros of the quadratic polynomial f x is equal to 6 X square + X - 2 then find the value of Alpha minus beta

Asked by rashirohaanbansal | 10th May, 2021, 04:54: PM

Expert Answer:

Given: f(x) = 6x2 + x - 6
As space straight alpha space and space straight beta space are space the space zeros space of space the space quadratic space polynomial space straight f left parenthesis straight x right parenthesis comma space we space have
straight alpha plus straight beta equals negative 1 over 6 space space and space space αβ equals negative 2 over 6 equals negative 1 third
Now comma
open parentheses straight alpha minus straight beta close parentheses squared equals open parentheses straight alpha plus straight beta close parentheses squared minus 4 αβ
equals open parentheses negative 1 over 6 close parentheses squared minus 4 open parentheses negative 1 third close parentheses squared
equals 1 over 36 minus 4 over 9
equals fraction numerator 1 minus 16 over denominator 36 end fraction
equals negative 15 over 36
equals negative 5 over 12

Answered by Renu Varma | 11th May, 2021, 11:14: AM