Question

The sum of the roots of the equation 2x square -5x+3=0

Answer 1

Given:

equation: 2x² -5x+3=0

To Find:

the sum of its roots

Solution:

$\sf {\underline{★According \: to \: the \: question : }}$

now we have to factorise the equation to find the roots

let's start :

$: \implies \sf \: {2x}^{2} - 5x + 3 \: \: \: \: \: \: \: \: \: \: \: \\ \\: \implies \sf \: {2x}^{2} - 3x - 2x + 3 \: \: \\ \\ : \implies \sf \:x(2x - 3)1(2x - 3) \\ \\ : \implies \sf \:(2x - 3)(x + 1) \: \: \: \: \: \: \:$

$\tt {\blue{roots : }}$

$: \implies \sf2x - 3 = 0 \\ \\ : \implies \sf \:2x = 3 \: \: \: \: \: \: \\ \\ : \implies \sf \:x = \frac{3}{2} \: \: \: \: \: \:$

$: \implies \sf \:x + 1 = 0 \\ \\: \implies \sf \:x = - 1 \: \: \: \:$

sum:

$: \implies \sf \:\frac{3}{2} + ( - 1) \\ \\: \implies \sf \: \frac{3}{2} - 1 \: \: \: \: \: \: \\ \\ : \implies \sf \: \frac{3}{2} - \frac{2}{2} \: \: \: \\ \\ : \implies \sf { \boxed {\frac{1}{2} }}\pink★ \: \: \: \: \: \:$

hope this helps.!!