Question

Rounded to the nearest hundredth, what is the positive solution to the quadratic equation 0 = 2x2 + 3x – 8?

Answer 1

2x² + 3x -8 = 0

a = 2 , b = 3 , c = -8
So..
D = b²-4ac = 9 + 64 = 73

for bigger solution , use x = -b + √D / 2a
For smaller solution, use x = -b - √D / 2a

So
= -3 + √73 / 2. 2
= 1/4 (√73 -3)

Hopefully helpfull.. ^_^

Answer 2

Answer:  The required positive solution is  x = 1.3.

Step-by-step explanation:  We are given to find the positive solution of the following quadratic equation:

$2x^2+3x-8=0~~~~~~~~~~~~~~~~~~(i)$

The solution set of the quadratic equation $ax^2+bx+c=0,~~a\neq 0$ is given by

$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}.$

From equation (i), we have

a = 2,  b = 3  and  c = -8.

Therefore, the solution set of equation (i) is given by

$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\\\Rightarrow x=\dfrac{-3\pm\sqrt{3^2-4\times 2\times (-8)}}{2\times 2}\\\\\\\Rightarrow x=\dfrac{-3\pm\sqrt{9+64}}{4}\\\\\\\Rightarrow x=\dfrac{-3\pm\sqrt{67}}{4}\\\\\Rightarrow x=\dfrac{-3+\sqrt{67}}{4},~~~x=\dfrac{-3-\sqrt{67}}{4}\\\\\\\Rightarrow x=\dfrac{-3+8.18}{4},~~\Rightarrow x=\dfrac{-3-8.18}{4}\\\\\\\Rightarrow x=\dfrac{5.18}{4},~~\Rightarrow x=-\dfrac{11.8}{4}\\\\\\\Rightarrow x=1.295,~~~~~\Rightarrow x=-2.95.$

So, the required positive solution is  x = 1.295.

Rounding to nearest hundredth, we get x = 1.3.

Thus, the required positive solution is  x = 1.3.