Question

If alpha and beta are zeroes of the polynomial 2x^2-5x+3 , find the values of

I) alpha^2+beta^2
ii)1/2alpha+1/2beta
III)alpha/beta+beta/alpha
iv)alpha^3+beta^3​

Answer 1

$2 {x}^{2} - 5x + 3 \\ 2 {x}^{2} - 2x - 3x + 3 \\ 2x(x - 1) - 3(x - 1) \\ (2x - 3)(x - 1) \\ x = \frac{3}{2} \: \: \: x = 1 \\ \alpha = \frac{3}{2} \: \: \: \: \: \: \beta = 1 \\ { \alpha }^{2} + { \beta }^{2} = { \frac{3}{2} }^{2} + {1}^{2} \\ = \frac{9}{4} + 1 \\ = \frac{13}{4}$

Answer 2

Answer:1st and is 3.25

2nd ans is 1.25

3rd ans is 2.1667

4th ans is 4.375

Step-by-step explanation: firstly we find the valve of alpha and beta by quadratic equation which comes out to be 1.5 and 1 once valve of alpha and beta are obtain ans can be obtain