Answer:
x = - 2√2
x = -2
Step-by-step explanation:
A . 5 + x² = 2 x² +13
5 + x² - 2 x² - 13 = 0
- x² -8 = 0
- x² = 8
x² = -8
x = - √8
x = - 2√2
B . 5 + x³ = 2 x³ + 13
5 + x³- 2 x³ - 13 = 0
- x³ -8 = 0
-x³ = 8
x³ = -8
x = - ∛8
x = -2
Given:
The graph of a polynomial.
To find:
The number of roots of the polynomial lie between x = -4 and x = 3.
Solution:
From the given graph it is clear that the graph is a downward U-shaped curve. It means the given graph represents a quadratic polynomial.
The graph of the polynomial is below the x-axis immediate before x=-2 and above the x-axis immediate after x=-2. It means the graph intersect the x-axis at x=-2.
The graph of the polynomial is above the x-axis immediate before x=2 and below the x-axis immediate after x=2. It means the graph intersect the x-axis at x=2.
Since the graph of the polynomial divides the x-axis two times between x = -4 and x = 3, therefore the two roots of the polynomial lie between x = -4 and x = 3.