Question

2/x-3+x/2=-1/2 transform to quadratic equations

Answer 1

2/x-3 + x/2 = -1/2

4+x²-3x / 2(x-3) = -1/2

2(x²-3x+4 ) = -2(x-3)

x²-3x+4= -(x-3)

x²-3x +x -3 =0

x² -2x -3 =0

comparing this eq with standard form of quadratic equation ax²+bx+c=0

hence it is quadratic equation

Answer 2

Given: Given function is 2/x-3+x/2=-1/2

To find: We have to transform it to quadertic equation.

Solution:

The expression is 2/x-3+x/2=-1/2.

The general quadratic form of a equation is-

$a {x}^{2} + bx + c$

At first we have to bring all the x related terms to left side and all numbers to right side.

$\frac{2}{x} + \frac{x}{2} = - \frac{1}{2} + 3 \\ \frac{2}{x} + \frac{x}{2} = \frac{5}{2} \\ \frac{4 + {x}^{2} }{2x} = \frac{5}{2}$

Cross multiplying we get-

$8 + 2{x}^{2} = 10x$

Arranging the expression we get-

$2 {x}^{2} - 10x + 8 = 0 \\ {x}^{2} - 5x + 4 = 0$

The quadratic equation is

${x}^{2} - 5x + 4 = 0$