Question

Find out for what value of the variable:

do the trinomial a2+7a+6 and the binomial a+1 have the same value?

do the trinomial 3x2−x+1 and the trinomial 2x2+5x−4 have the same value?

Answer 1

`a=-1,\ a=-5`

`x=-2+i,\ -2-i`

Explanation:

Equations

We have two cases where some variable is required to be found such that some condition is met. The first case is about finding the value of a that complies:

`a^2+7a+6=a+1`

Rearranging

`a^2+6a+5=0`

Factoring:

`(a+1)(a+5)=0`

There are two solutions:

`a=-1,\ a=-5`

The second case requires us to find the value of x such that

`3x^2-x+1 =2x^2+5x-4`

Rearranging

`x^2+4x+5=0`

This second-degree equation has no real roots. We'll offer the imaginary (complex) solutions:

`x=-2+i,\ -2-i`