Question

If α,β are the zeroes of 2x²-7x+3,find the value of α²+β².

Answer 1

$\huge\mathfrak\red{Answer}$

THERE ARE TWO WAYS TO SOLVE SUCH TYPE OF QUESTIONS .

YOU CAN CHOOSE ACCORDING TO YOUR CONVENIENCE.

$2 {x}^{2} - 7x + 3 = 0 \\ 2 {x}^{2} - 6x - x + 3 = 0 \\ 2x(x - 3) - 1(x - 3) = 0 \\ (x - 3)(2x - 1) = 0 \\ \alpha = 3 \: \ \\ \beta = \frac{1}{2} \\ \\ { \alpha }^{2} + { \beta }^{2} = ({3})^{2} + ( { \frac{1}{2} })^{2} \\ { \alpha }^{2} + { \beta }^{2} = 9 + \frac{1}{4} \\ { \alpha }^{2} + { \beta }^{2} = \frac{37}{4} \\ \\ method \: (2) \\ { \alpha }^{2} + { \beta }^{2} = {( \alpha + \beta )}^{2} - 2 \alpha \beta \\ { \alpha }^{2} + { \beta }^{2} = ({ \frac{7}{2} })^{2} - 2( \frac{3}{2} ) \\ \\ { \alpha }^{2} + { \beta }^{2} = \frac{49}{4} - 3 \\ \\ { \alpha }^{2} + { \beta }^{2} = \frac{49 - 12}{4} \\ \\ { \alpha }^{2} + { \beta }^{2} = \frac{37}{4} \\ \\ \\ concept \: used \\ \\ sum \: of \: roots = \frac{ - b}{a} \\ product \: of \: roots \: = \frac{c}{a} \\ \\ a = 2 \\ b = - 7 \\ c = 3 \\ acc \: to \: equation$