Question

write two numbers that multiply to the value on top and add to the value on bottom. answer attempt 1 out of 2 4 + × -21

Explanation:

Step1: Let the two - numbers be \(x\) and \(y\).

We have the equations \(x\times y=- 21\) and \(x + y = 4\). From \(x + y=4\), we get \(y = 4 - x\).

Step2: Substitute \(y = 4 - x\) into the product equation.

\(x(4 - x)=-21\), which expands to \(4x-x^{2}=-21\), or \(x^{2}-4x - 21=0\).

Step3: Factor the quadratic equation.

For the quadratic equation \(ax^{2}+bx + c = 0\) (here \(a = 1\), \(b=-4\), \(c=-21\)), we need to find two numbers that multiply to \(ac=-21\) and add up to \(b = - 4\). The factored form of \(x^{2}-4x - 21=0\) is \((x - 7)(x+3)=0\).

Step4: Solve for \(x\).

Setting each factor equal to zero gives \(x - 7=0\) or \(x + 3=0\). So \(x = 7\) or \(x=-3\).
If \(x = 7\), then \(y=4 - 7=-3\); if \(x=-3\), then \(y=4-(-3)=7\).

Answer:

7 and - 3