Question

Write an equation in which the quadratic expression x^2+x-30 equals 0.
Write the trinomial in factored form
Solve for x and explain what your answers mean.

Answer 1

Answer:

The trinomial in factored form is:

$(x+6)(x-5)=0$

The solutions are;

$x=-6\: or\:x=5$

The graph intersects the x-axis at $x=-6\: and\:x=5$

Step-by-step explanation:

The required equation is;

$x^2+x-30=0$

We split the middle term to get;

$x^2+6x-5x-30=0$

We factor by grouping;

$x(x+6)-5(x+6)=0$

The trinomial in factored form is:

$(x+6)(x-5)=0$

Use the zero product principle;

$(x+6)=0\: or\: (x-5)=0$

$x=-6\: or\:x=5$

These are the x-intercepts of the graph of the corresponding quadratic function.

Or the zeros/roots/solutions of the equation.