Question

Which are the solutions of x2 = –11x+4?

a. -11 - √137/2 , -11+√137/2
b. -11 - √125/2 , -11+√125/2
c. 11 - √137/2 , 11+√137/2
d. 11 - √125/2 , -11+√125/2

Answer 1

The solutions of x² = -11x + 4 are 0.377 and 10.377

None of the given options is correct

Step-by-step explanation:

To find the solutions of the equation
`\(x^2 = -11x + 4\)`, we can use the quadratic formula. The quadratic formula states that for an equation in the form
`\(ax^2 + bx + c = 0\)`, the solutions for
`\(x\)` are given by:

`\[x = (-b \pm √(b^2 - 4ac))/(2a)\]`

Comparing the given equation
`\(x^2 = -11x + 4\)` with the standard form
`\(ax^2 + bx + c = 0\)`, we have
`\(a = 1\), \(b = -11\)`, and
`\(c = 4\).`

Substituting these values into the quadratic formula, we get:

`\[x = (-(-11) \pm √((-11)^2 - 4(1)(4)))/(2(1))\]`

Simplifying this equation further:

`\[x = (11 \pm √(121 - 16))/(2)\]`

`\[x = (11 \pm √(105))/(2)\]`

Now, let's calculate the value of
`\(√(105)\)`:

`\[√(105) \approx 10.246\]`

So, the solutions for x are:

`\[x = (11 \pm 10.246)/(2)\]`

`\\\[x_1 \approx (11 - 10.246)/(2) \approx 0.377\]`

`\[x_2 \approx (11 + 10.246)/(2) \approx 10.377\]`

Therefore, none of the given options (a, b, c, d) matches the correct solutions for the equation
`\(x^2 = -11x + 4\).`