Question

what are the zeros of the function defined by the expression \\(x^2 - 7x - 30\\)?
answer
3 and -10
10 and -3
15 and 2
15 and -2
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Explanation:

Step1: Factor the quadratic

To find the zeros of \(x^2 - 7x - 30\), we factor it. We need two numbers that multiply to \(-30\) and add to \(-7\). The numbers are \(-10\) and \(3\)? Wait, no, let's check: \(10\) and \(-3\) multiply to \(-30\) and add to \(7\)? Wait, no, wait: \(x^2 -7x -30\). Let's factor: find \(a\) and \(b\) such that \(a \times b = -30\) and \(a + b = -7\). Let's see: \( -10\) and \(3\): \(-10 \times 3 = -30\), \(-10 + 3 = -7\). Wait, no, the quadratic is \(x^2 -7x -30\), so factoring: \((x - 10)(x + 3)\)? Wait, no: \((x - 10)(x + 3) = x^2 + 3x -10x -30 = x^2 -7x -30\). Wait, no, that's correct? Wait, no: \((x - 10)(x + 3) = x^2 + 3x -10x -30 = x^2 -7x -30\). Wait, but when we set to zero: \(x - 10 = 0\) gives \(x = 10\), \(x + 3 = 0\) gives \(x = -3\). Wait, but let's check the options. The options are 10 and -3. Wait, let's verify by plugging in. Let's take \(x = 10\): \(10^2 -7(10) -30 = 100 -70 -30 = 0\). \(x = -3\): \((-3)^2 -7(-3) -30 = 9 +21 -30 = 0\). So the zeros are 10 and -3.

Step2: Check the options

The option with 10 and -3 is one of the choices.

Answer:

10 and -3 (the option labeled "10 and -3")