1. Write a quadratic polynomial whose zeroes are ( root 2 + 1) ( root 2 - 1).

2.Show that one zero of 8x^{2}+30x+27 is the square of the other.

3.If one zero of the polynomial 2x^{2}+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*) = *x*^{2 }- **S***x* + **P**

= *x*^{2 }- 2√2*x *+ 1

(2). Please follow the given link :

(3). Please follow the given link :

**
**