Question

if a and b are the zeroes of the polynomial 2x^2+5x+1,then what is the value of a+b+ab?​

Answer 1

A and B are the zeroes of p(x)

p(x) = 2x² + 5x + 1

==> 2x² + 5x + 1

On comparing :

a = 2 ; b = 5 ; c = 1

By Quadratic Formula:

a,b = - b ± √D / 2a

==> - 5 ± √25 - 8 / 4

==> -5 ± √17 / 4

a = -5 + √17 / 4 , b = - 5 - √17 / 4

==> a + b + ab == ??

==> (-5 + √17) / 4 + (-5 - √17)/4 + (-5 + √17)/4 × (-5 - √17)/4

==> (-5 + √17 - 5 - √17)/4 + ( -5 + √17)( -5 - √17) / 16

==> ( 25 + 5√17 - 5√17 - 17 ) / 16

==> ( 25 - 17 ) / 16

==> 8 / 16

==> 1/2

Answer: 1 / 2