If you double the length of each side of a cube its surface area increases by what factor?
1 answer:
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If a binomial x-a is a factor of a polynomial p(x), then p(a)=0.
x+2 is a factor of p(x)=x³-6x²+kx+10, so p(-2)=0.
x+2 is a factor of p(x)=x³-6x²+kx+10, so p(-2)=0.
The polynomial equation <u>x³ - 4x² - 7x + 28 = 0</u>, has solutions <u>-√7, √7,</u> and <u>4</u>, among which <u>√7</u> and <u>4</u> are positive real solutions. Hence we have two positive real solutions. Hence, <u>option D</u> is the right choice.
In the question, we are asked for the number of positive real solutions for the polynomial equation, x³ - 4x² - 7x + 28 = 0.
To find the solutions, we do as follows:
x³ - 4x² - 7x + 28 = 0,
or, (x³ - 7x) - (4x² + 28) = 0 {Grouping},
or, x(x² - 7) - 4(x² - 7) = 0 {Taking common},
or, (x - 4)(x² - 7) = 0 {Grouping},
or, (x - 4)(x + √7)(x - √7) = 0 {Using the formula: }.
By the zero-product rule, the solutions are:
x - 4 = 0, or, x = 4,
x + √7 = 0, or, x = -√7,
x - √7 = 0, or, x = √7.
Thus, the positive real solutions are 4, and √7. Hence, there are two positive real solutions.
Thus, the polynomial equation <u>x³ - 4x² - 7x + 28 = 0</u>, has solutions <u>-√7, √7,</u> and <u>4</u>, among which <u>√7</u> and <u>4</u> are positive real solutions. Hence we have two positive real solutions. Hence, <u>option D</u> is the right choice.
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The complete question is:
"Which of the following expresses the possible number of positive real solutions for the polynomial equation shown below?
x³-4x²-7x+28=0
a. two or zero
b. three or one
c. one
d. two"
Answer to A:
16.67%
Explanation to A:
If we need a number greater than five, the only number left is six, meaning there is
We can make it a percent by moving the decimal two places to the right and rounding to the thousandths place (two numbers). This would make our final answer 16.67%
Answer to B:
50%
Explanation to B:
There are three even numbers: 2, 4, and 6. This means we have a chance to land on one.
0.5 = 50%