X squared plus 7x plus 6 equals 0?

Answer 1

1

*****

1 is not correct.

The correct solution is x = -1 or -6.

You can easily find it this way:

Factorising, we obtain

x2 + 7x + 6 = (x + 1)(x + 6) = 0.

The above is true if, and only if, either,

x + 1 = 0, or, else,

x + 6 = 0; that is, if

x = -1 or -6, which is the answer we sought.

The rule is that two numbers multiply to give a product of zero, if, and only if, one of the two numbers is zero.

To check our answer, let's try substitution into the original equation:

Does (-1)2 + 7(-1) + 6 = 0?

We see that 1 - 7 + 6 = 0.

Does (-6)2 + 7(-6) + 6 = 0?

We see that 36 - 42 + 6 = 0.

The answer is yes, both times, thus assuring us that we have found the correct answer.