Answer:
8) -8, -9
9) 4, [tex]$ \frac{1}{2} $[/tex]
Step-by-step explanation:
8) x² + 12x + 27
Solutions of a polynomial means the values of [tex]$ x $[/tex] such that the polynomial becomes zero. [tex]$ i.e., y = 0 $[/tex].
We use the following formula to determine the solutions of a quadratic equation of the form: [tex]$ ax^2 + bx + c = 0 $[/tex]
[tex]$ \implies x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $[/tex]
In this equation, [tex]$ a = 1; b = 12; c = 27 $[/tex]
Substituting in the formula, we have:
[tex]$ x = \frac{-12 \pm \sqrt{144 - 108}}{2} $[/tex]
[tex]$ \implies x = \frac{-12 \pm 6}{2} $[/tex]
Taking 2 common outside we get:
[tex]$ x = - 6 \pm 3 $[/tex]
Therefore, we get two solutions viz, x = -3, -9.
9) 2x² - 9x + 4 = y
X- intercepts of a polynomial means the value of x such that y = 0. It means the roots of the polynomial.
Solving the equation using the formula above, we get:
[tex]$ x = \frac{-(-9) \pm \sqrt{81 - 32}}{2(2)} $[/tex]
[tex]$ \implies x = \frac{9 \pm 7}{4} $[/tex]
The values of x = 4, [tex]$ \frac{1}{2} $[/tex].
Hence, the answer.
