Compare the volumes of Prism A and Prism B.
1 answer:
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The values of k for the different quadratic equation solutions are as follows
a the equation 2x² - x + 3k = 0 has two distinct real roots
- k < 1/24
b. the equation 5x² - 2x + (2k − 1) = 0 has equal roots
- k = 3/5
ci the equation -x² + 3x + (k + 1) = 0 has real roots
- k > -3.25
d the equation 3kx² - 3x + 2 = 0 has no real solutions
- k < ± 1.633
Quadratic equations of the form ax² + bx + c = 0 is solved using the formula
OR
The equation b² - 4ac is called the discriminant and it is used as follows
To solve the equation and get two real roots: 2x² - x + 3k = 0
- b² - 4ac > 0
substituting the values gives
(-1)² - 4 * 2 * 3k > 0
1 - 24k > 0
1 > 24k
divide through by coefficient of k
k < 1/24
To solve the equation and get equal roots: 5x² - 2x + (2k − 1) = 0
- b² - 4ac = 0
substituting the values gives
(-2)² - 4 * 5 * (2k - 1) = 0
4 - 40k + 20 = 0
-40k = -24
divide through by coefficient of k
k = 3/5
To solve the equation and get real roots -x² + 3x + (k + 1) = 0
- b² - 4ac > 0
substituting the values gives
(3)² - 4 * -1 * (k+1) > 0
9 + 4k + 4> 0
4k > -13
divide through by coefficient of k
k > -3.25
To solve the equation and get no real solutions 3kx² - 3x + 2 = 0
- b² - 4ac < 0
substituting the values gives
(-3)² - 4 * 3k * 2 < 0
9 - 24k² > 0
9 > 24k²
divide through by coefficient of k²
k² < 24/9
k < ± 1.633
Learn more about roots of quadratic equations: brainly.com/question/26926523
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Answer:
<em><u>Linear function :</u></em>The characteristic property of linear functions is that when the input variable is changed, the change in the output is proportional to the change in the input. Linear functions are related to linear equations.
Step-by-step explanation:
We have
y=mx+c
for 1st
not satisfied.
for
2nd
not satisfied
<em><u>3rd</u></em>
<em><u>3rd satisfied</u></em>
4th
[note : substitute value of x to get value of y from table]
so
<u>t</u><u>h</u><u>i</u><u>r</u><u>d</u><u> </u><u>table represents a linear function.</u>
