Question

Use the quadratic f(x)=x²+3x-4 and use any method to solve for the Zeros. Use the same function to solve for x when y is 6. F(x)=6 Last, solve f(x)=10 for x.

Answer 1

a)
`f(x) = (x+4)\cdot (x-3)`, b)
`x = -5` or
`x = 2`, c)
`x \approx 2.531` or
`x \approx -5.531`

Explanation:

a) The function is solved by factorization:

`f(x) = (x+4)\cdot (x-3)`

b) The function has the following form:

`x^(2) + 3\cdot x - 4 = 6`

`x^(2) + 3\cdot x - 10 = 0`

The roots of the polynomial are found by factorization:

`(x+5)\cdot (x-2) = 0`

`x = -5` or
`x = 2`

c) The function has the following form:

`x^(2) + 3\cdot x - 4 = 10`

`x^(2) + 3\cdot x - 14 = 0`

The roots of the polynomial are determined by the General Formula for the Second-Order Polynomial:

`x_(1) = \frac{-3+\sqrt{3^(2)-4\cdot (1)\cdot (-14)}}{2\cdot (1)}`

`x_(1) \approx 2.531`

`x_(2) = \frac{-3-\sqrt{3^(2)-4\cdot (1)\cdot (-14)}}{2\cdot (1)}`

`x_(2) \approx -5.531`