if the squared difference of the zeroes of the quadratic polynomil f(x)=x square+px+45 is equal to 144,then find the value of p?

in this answer how 4ab comes?

Asked by ketanjain.2502 | 14th May, 2019, 12:09: PM

Expert Answer:

begin mathsize 16px style straight f left parenthesis straight x right parenthesis space equals space straight x squared space plus px space plus space 45
Here space straight a space equals space 1 comma space straight b space equals space straight p space and space straight c space equals space 45.

straight alpha space plus space straight beta space equals space fraction numerator negative straight b over denominator straight a end fraction space equals space fraction numerator negative straight p over denominator 1 end fraction space equals space minus straight p
αβ space equals space straight c over straight a space equals space 45 over 1 equals space 45
open parentheses straight alpha space minus space straight beta space close parentheses squared space equals space open parentheses straight alpha space plus space straight beta space close parentheses squared space minus space 4 αβ
bold rightwards double arrow bold space bold 144 bold space bold space bold space bold space equals space open parentheses straight alpha space plus space straight beta space close parentheses squared space minus space 4 αβ space space space space..... given space
rightwards double arrow space 144 space space space space equals open parentheses negative straight p space close parentheses squared space minus space 4 space cross times space 45
rightwards double arrow space 144 space space space space space equals space straight p squared space minus space 180
rightwards double arrow space straight p squared space space space space space space space equals space 324
rightwards double arrow space straight p space space space space space space space space space equals space plus-or-minus 18 end style
 

Answered by Yasmeen Khan | 14th May, 2019, 01:55: PM