Question

Please answer these question:
1. Factorise: a. 9t²-6t+1
b. 3x²-2
2. If α and β are the zeros of the polynomials x²+6x+9 then form a polynomials whose zeros are -α and -β.

Answer 1

(1)

(a)  Given Equation is 9t^2 - 6t + 1.

9t^2 - 3t - 3t + 1

3t(3t - 1) - 1(3t - 1)

(3t - 1)(3t - 1)

(3t - 1)^2.


(b) 3x^2 - 2

$( \sqrt{3}x)^2 - ( \sqrt{2} )^2$

$( \sqrt{3} x + \sqrt{2} )( \sqrt{3}x - \sqrt{2} )$




(2) 

Note: I am writing Alpha and Betas as a and b. Because It is difficult for me to write always.

Given Equation is x^2 + 6x + 9.

it is in the form os ax^2 + bx + c = 0

where a = 1, b = 6, c = 9.

We know that sum of the roots = $\frac{-b}{a}$

                                                    = $\frac{-6}{1}$

                            a + b = -6



We know that product of the roots = $\frac{c}{a}$

                                                          = $\frac{9}{1}$

                         a * b = 9


Now,

The equation of the polynomial = $x^2 + (a + b)x + a * b$

                                                     $= x^2 + (-6)x + 9$

                                                     x^2 - 6x + 9.


Hope this helps!