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

Answer:

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

Step-by-step 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:

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

$x_{1} \approx 2.531$

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

$x_{2} \approx -5.531$