What is a so the polynomial p(x)= (a+1)x^2 + 2ax + (a+2) has two roots?
1 answer:
Answer:
a < -
Step-by-step explanation:
Using the discriminant Δ = b² - 4ac
For a polynomial to have 2 real roots
b² - 4ac > 0
Given
p(x) = (a + 1)x² + 2ax + (a + 2)
with a = a + 1, b = 2a and c = a + 2, then
(2a)² - 4(a + 1)(a + 2) > 0 ← expand and simplify left side
4a² - 4(a² + 3a + 2) > 0
4a² - 4a² - 12a - 8 > 0
- 12a - 8 > 0 ( add 8 to both sides )
- 12a > 8
Divide both sides by - 12, reversing the symbol as a result of dividing by a negative quantity
a < , that is
a < -
You might be interested in
Answer:
We conclude that the population mean is 24.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 24
Sample mean, = 22.8
Sample size, n = 100
Alpha, α = 0.05
Sample standard deviation, s = 8.3
First, we design the null and the alternate hypothesis
We use Two-tailed z test to perform this hypothesis.
Formula:
Putting all the values, we have
We calculate the p-value with the help of standard z table.
P-value = 0.1498
Since the p-value is greater than the significance level, we accept the null hypothesis. The population mean is 24.
Now,
Since, the z-statistic lies in the acceptance region which is from -1.96 to +1.96, we accept the null hypothesis and conclude that the population mean is 24.