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Shkiper50 [21]
3 years ago
13

Does anyone know the answer to these two problems?

Mathematics
1 answer:
Nady [450]3 years ago
8 0

Answer:

8) -8, -9

9) 4, $ \frac{1}{2} $

Step-by-step explanation:

8) x² + 12x + 27

Solutions of a polynomial means the values of $ x $ such that the polynomial becomes zero. $ i.e., y = 0 $.

We use the following formula to determine the solutions of a quadratic equation of the form: $ ax^2 + bx + c = 0 $

    $ \implies x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $

In this equation, $ a = 1; b = 12; c = 27 $

Substituting in the formula, we have:

$ x = \frac{-12 \pm \sqrt{144 - 108}}{2} $

$ \implies x = \frac{-12 \pm 6}{2} $

Taking 2 common outside we get:

$ x = - 6 \pm 3 $

Therefore, we get two solutions viz, x = -3, -9.

9) 2x² - 9x + 4 = y

X- intercepts of a polynomial means the value of x such that y = 0. It means the roots of the polynomial.

Solving the equation using the formula above, we get:

$ x = \frac{-(-9) \pm \sqrt{81 - 32}}{2(2)} $

$ \implies x = \frac{9 \pm 7}{4} $

The values of x = 4, $ \frac{1}{2} $.

Hence, the answer.

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