Question

What two numbers multiply to -30 and add to 1?

Answer 1

These numbers would be -5 & 6...

(-5)(6) = -30
-5 + 6 = 1

Answer 2

The products of two numbers involves multiplying them.

The two numbers are -5 and 6

Let the numbers be x and y.

So, we have:

$\mathbf{x \times y = -30}$

$\mathbf{x + y = 1}$

Make x the subject in $\mathbf{x + y = 1}$

$\mathbf{x = 1 - y}$

Substitute $\mathbf{x = 1 - y}$ in $\mathbf{x \times y = -30}$

$\mathbf{(1 - y)y = -30}$

Expand

$\mathbf{y - y^2 = -30}$

So, we have:

$\mathbf{y^2 -y - 30 = 0}$

Expand

$\mathbf{y^2 -6y + 5y - 30 = 0}$

Factorize

$\mathbf{y(y -6) + 5(y - 6) = 0}$

Factor out y - 6

$\mathbf{(y + 5) (y - 6) = 0}$

Solve for y

$\mathbf{y = -5\ and\ 6}$

Hence, the two numbers are -5 and 6

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