1. Write a quadratic polynomial whose zeroes are ( root 2 + 1) ( root 2 - 1).
2.Show that one zero of 8x2+30x+27 is the square of the other.
3.If one zero of the polynomial 2x2+3x+lamda= 1/2,find the value of lamda and the other zero.
(1). The given zeroes are √2 + 1 and √2 - 1.
sum of zeroes = S = (√2 + 1) + (√2 - 1) = √2 + 1 + √2 - 1 = 2√2
product of zeroes = P = (√2 + 1)(√2 - 1) = 2 - 1 = 1
So, the required quadratic polynomial is given by,
p (x) = x2 - Sx + P
= x2 - 2√2x + 1
(2). Please follow the given link :
(3). Please follow the given link :