Question Find the equation with zeros at -3 and 4: $x^2 - x - 12 = 0$

Studdy Solution

STEP 1

Assumptions
1. Zeros of a polynomial are the values of $x$ for which the polynomial equals zero.
2. The given zeros are $x = -3$ and $x = 4$ .
3. We are looking for a quadratic equation of the form $ax^2 + bx + c = 0$ that has these zeros.

STEP 2

If a quadratic equation has zeros at $x = -3$ and $x = 4$ , it can be factored into the form $(x + 3)(x - 4) = 0$ .

STEP 3

Expand the factored form to find the quadratic equation.
$(x + 3)(x - 4) = x^2 - 4x + 3x - 12$

STEP 4

Combine like terms in the expanded form.
$x^2 - 4x + 3x - 12 = x^2 - x - 12$

STEP 5

Now we have the quadratic equation in standard form.
$x^2 - x - 12 = 0$

STEP 6

Match the obtained quadratic equation with the given options.
The correct equation is $x^2 - x - 12 = 0$ .

STEP 7

Identify the correct option based on the equation found in STEP_6.
The correct option is D. $x^{2}-x-12=0$ .

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