Question

What are the exact solutions of x^2 − 3x − 7 = 0?

Answer 1

Given:

The given equation is
`x^(2) -3x-7=0`

We need to determine the exact solutions of the equation.

Exact solution:

The exact solution of the equation can be determined by solving the equation using quadratic formula,

`x=(-b \pm √(b^2-4ac))/(2a)`

From the equation the values are a = 1, b = -3 and c = -7

Thus, substituting these values in the equation, we get;

`x=(-(-3) \pm √(3^2-4(1)(-7)))/(2(1))`

`x=(3 \pm √(9+28))/(2)`

`x=(3 \pm √(37))/(2)`

Thus, the exact solutions of the given equation is
`x=(3 \pm √(37))/(2)`

Hence, Option A is the correct answer.