Question

Does anyone know the answer to these two problems?

Answer 1

8) -8, -9

9) 4,
`$ (1)/(2) $`

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 = (-b \pm √(b^2 - 4ac))/(2a) $`

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

Substituting in the formula, we have:

`$ x = (-12 \pm √(144 - 108))/(2) $`

`$ \implies x = (-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 = (-(-9) \pm √(81 - 32))/(2(2)) $`

`$ \implies x = (9 \pm 7)/(4) $`

The values of x = 4,
`$ (1)/(2) $`.

Hence, the answer.