Question

Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.

Answer 1

Given:

The quadratic equation is:

`10m^2-7m+3=0`

To find:

The solutions for the given equation by using the quadratic formula.

Solution:

If a quadratic equation is
`ax^2+bx+c=0`, then the quadratic formula is:

`x=(-b\pm √(b^2-4ac))/(2a)`

We have,

`10m^2-7m+3=0`

Here,
`a=10,b=-7,c=3`. Using the quadratic formula, we get

`m=(-(-7)\pm √((-7)^2-4(10)(3)))/(2(10))`

`m=(7\pm √(49-120))/(20)`

`m=(7\pm √(-71))/(20)`

`m=(7\pm i√(71))/(20)`
`[\because √(-a)=i√(a),a>0]`

Therefore, the solution set of the given equation is
`\left\{(7- i√(71))/(20),(7+ i√(71))/(20)\right\}`. Hence, the correct option is D.