Question

Find the zeros of y= x - 4x - 9 by completing the square.

Answer 1

The zeros for the given equation are A. $x = {2 \pm \sqrt{13}}.$

Step-by-step explanation:

Step 1:

To solve for x in a polynomial equation, we use the formula

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}.$

Here a is the coefficient of $x^{2}$, b is the coefficient of $x$ and c is the coefficient of the constant term.

In the given equation, $a = 1, b = -4, c = -9$.

Step 2:

Substituting the values of a, b, and c in the equation, we get

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a} =\frac{-(-4) \pm \sqrt{(-4)^{2}-4 (1)(-9)}}{2 (1)} = \frac{4 \pm \sqrt{(16+36}}{2 }.$

$\frac{4 \pm \sqrt{(16+36}}{2 } = \frac{4 \pm \sqrt{(52}}{2 } = \frac{4 \pm2 \sqrt{(13}}{2 }= {2 \pm \sqrt{13}}.$

So the answer is option A. $x = {2 \pm \sqrt{13}}.$