Question

Rounded to the nearest hundredth , what is the positive solution to the quadratic equation 0=2x^2+3x-8

Answer 1

The positive solution to the quadratic equation
`2 x^(2)+3 x-8=0` is x = 1.39

Solution:

Given quadratic equation is
`2 x^(2)+3 x-8=0`

The general quadratic equation is of form:

`a x^(2)+b x+c=0`

Now comparing the general equation with the given equation we get

a = 2 , b = 3 and c = -8

The formula to determine roots of the quadratic equation is:

`x=\frac{-b \pm \sqrt{b^(2)-4 a c}}{2 a}`

On plugging in vlaues, we get

`x=\frac{-3 \pm \sqrt{3^(2)-4 * 2 *(-8)}}{2 * 2}`

`\mathrm{x}=(-3 \pm √(9-(-64)))/(4)`

On solving we get,

`\begin{array}{l}{\mathrm{x}=(-3 \pm √(9+64))/(4)} \\\\ {\mathrm{x}=(-3 \pm √(73))/(4)}\end{array}`

`\mathrm{x}=(-3+√(73))/(4) \text { OR } \mathrm{x}=(-3-√(73))/(4)`

x = 1.39 OR x = -2.89

Hence , the positive solution to the quadratic equation is x = 1.39