1. Which of the following conclusions is true about the statement below ?
x^2 = square root x
A. The statement is never true.
B. The statement is true when x = 0.
C. The statement is true when x is negative.
D. The statement is always true.
My answer is c.
2. Select the approximate values of x that are solutions to f ( x ) = 0, where f (x)=-2 x^2 +4 x + 9.
A. (-0.22 , 0.44 0
B. (-2 , 4)
C. (-2.00 , -4.50 )
D. ( -1.35 , 3.35 )
My answer is B.
3. Select the approximate values of x that are solutions to f ( x ) = 0, where f ( x)= -3 x^2 + 8 x +3.
A. ( 3.00 , -0.33 )
B. ( -3 , 8 )
C. ( -2.67 , -1.00 )
D. ( -1.00 , 2.67 )
My answer is A.
4. Select the approximate values of x that are solutions to f (x)=0, where f(x)=8 x^2 +7 x +4 .
A. ( -0.39 , 1.27 )
B. ( -8 , 7 )
C. ( -0.88 , -0.50 )
D. ( -2.00 , 1.75)
My answer is C.
You score 1/4
1C incorrect
2B incorrect
3A correct
4C incorrect
Hi Graham
I went back over my work and
1. A
2. D
4. A
please let me know if I miss something! Thank you
Select the approximate values of x that are solutions to f(x) = 0, where
f(x) = -3x2 + 6x + 9
1. To determine the true conclusion about the statement x^2 = square root x, we can start by simplifying the equation. Squaring both sides of the equation gives us x^2 = x. Rearranging the terms, we have x^2 - x = 0. Factoring out an x, we get x(x - 1) = 0. Setting each factor equal to zero, we have x = 0 and x - 1 = 0, which gives us x = 0 and x = 1 as the solutions.
Based on this analysis, we can see that the statement x^2 = square root x is true when x = 0 and x = 1. Therefore, the correct conclusion is B. The statement is true when x = 0.
2. To find the approximate values of x that are solutions to f(x) = 0, where f(x) = -2x^2 + 4x + 9, we can use the quadratic formula. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions are given by:
x = [-b ± sqrt(b^2 - 4ac)] / (2a)
For our equation f(x) = -2x^2 + 4x + 9, we have a = -2, b = 4, and c = 9. Plugging these values into the quadratic formula, we get:
x = [-4 ± sqrt(4^2 - 4(-2)(9))] / (2(-2))
= [-4 ± sqrt(16 + 72)] / (-4)
= [-4 ± sqrt(88)] / (-4)
Simplifying further, we have:
x = [-4 ± sqrt(8 * 11)] / (-4)
= [-4 ± 2sqrt(11)] / (-4)
= 1 ± 0.632sqrt(11)
Approximating these values, we have x ≈ -2.26 and x ≈ 4.26. Therefore, the correct answer is D. (-1.35, 3.35).
3. Similarly, to find the approximate values of x that are solutions to f(x) = 0, where f(x) = -3x^2 + 8x + 3, we can use the quadratic formula. In this case, we have a = -3, b = 8, and c = 3. Plugging these values into the quadratic formula, we get:
x = [-8 ± sqrt(8^2 - 4(-3)(3))] / (2(-3))
= [-8 ± sqrt(64 + 36)] / (-6)
= [-8 ± sqrt(100)] / (-6)
= [-8 ± 10] / (-6)
Simplifying further, we have:
x = [-8 + 10] / (-6) or x = [-8 - 10] / (-6)
= 2 / (-6) or x = -18 / (-6)
= -1/3 or x = 3
Therefore, the correct answer is A. (3.00, -0.33).
4. Lastly, to find the approximate values of x that are solutions to f(x) = 0, where f(x) = 8x^2 + 7x + 4, we once again use the quadratic formula. Here, a = 8, b = 7, and c = 4. Plugging these values into the quadratic formula, we get:
x = [-7 ± sqrt(7^2 - 4(8)(4))] / (2(8))
= [-7 ± sqrt(49 - 128)] / (16)
= [-7 ± sqrt(-79)] / (16)
Since we have a negative value inside the square root, it indicates that there are no real solutions for the equation. Therefore, none of the given options (A, B, C, D) are correct choices for this particular question.