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\\eq 0` is given by

`x=(-b\pm√(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=(-b\pm√(b^2-4ac))/(2a)\\\\\\\Rightarrow x=(-3\pm√(3^2-4* 2* (-8)))/(2* 2)\\\\\\\Rightarrow x=(-3\pm√(9+64))/(4)\\\\\\\Rightarrow x=(-3\pm√(67))/(4)\\\\\Rightarrow x=(-3+√(67))/(4),~~~x=(-3-√(67))/(4)\\\\\\\Rightarrow x=(-3+8.18)/(4),~~\Rightarrow x=(-3-8.18)/(4)\\\\\\\Rightarrow x=(5.18)/(4),~~\Rightarrow x=-(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.