noimelastrilla
Answered

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1.What is the sum and product of the roots of the quadratic equation 4m2 -8m+8 = 0?
a. (Sum = -2, Product = -4)
C. (Sum = -2, Product = 4)
b. (Sum = 2, Product = 4)
d. (Sum = 2, Product = -4)
2.Determine the quadratic equation in standard form given the roots (5,0).
a. x2 - 5x - 5 = 0
c. x2 - 5x = 0
b. x2 - 5x + 5 = 0
d. x2 + 5x = 0
3.What do you call an expression that have a polynomial/ s in the numerator or denominator?
a. Rational algebraic Expression
b. Quadratic Equation
c. Linear Expression
d. Imaginary Expression
4.A rectangular garden has an area of 14m² and a perimeter of 18 meters. find the dimensions of the rectangular garden.
a. w² – 9w + 14 = 0
b. w² – 9w – 14 = 0
c. w² + 9w + 14 = 0
d. w² + 9w – 14 = 0
5.The product of two consecutive odd integers is 99. find the integers.
a. 9, 11 and –9, 11
b. 9, 11 and –9 and –11
c. –9, 11 and –9, –11
d. 9, –11 and –9 and 11
6.The product of two consecutive even integers is 168. find the integers.
a. 12, 14 and –12 and 14
b. –12, 14 and 12 and –14
c. –12, 14 and –12 and –14
d. 12, 14 and –12, –14
7.Find for the solutions of the equation x (x–5) = 36.
a. x = 9 or x = 4
b. x = 9 or x = –4
c. x = –9 or x = 4
d. x = –9 or x = –4
8.Which of the following equation is an example of a quadratic inequality?
a. x² – 4z + 4 > 0
b. 4m² – 8m = 12
c. 10x + 6 ≤ 0
d. 5x – 6 = 3
9.If the value of x in the quadratic inequality is greater than or greater than or equal to a certain number then the solutions is?
a. Toward each other on the number line
b. Values are in reverse side
c. Opposite directions on the number line
d. Values of x in the all negative
10.If the value of x in the quadratic inequality is less than or less than or yto a certain number then the solutions?
a. Toward each other on the number line
b. Values are in reverse side
c. Opposite directions on the number line
d. Values of x in the all negative
​

Sagot :

pvzzombs

Solution/s:

1. What is the sum and product of the roots of the quadratic equation [tex] 4m^2 - 8m + 8 = 0 [/tex]?

Solution:

Sum of the roots = [tex] \displaystyle -b/a = -(-8)/4 = 8/4 = \boxed{2} [/tex]

Product of the roots = [tex] \displaystyle c/a = 8/4 = \boxed{2} [/tex]

Unfortunately there are no real roots exists for the equation [tex] 4m^2 - 8m + 8 = 0 [/tex]. So it this still valid? Yes. Turns out that their complex solution has a sum of 2 and a product of 2.

2. Determine the quadratic equation in standard form given the roots [tex] (5,0) [/tex]

Solution:

[tex] \displaystyle x = -5, x = 0 [/tex]

[tex] \displaystyle x + 5 = 0, x = 0 [/tex]

[tex] \displaystyle (x + 5)x [/tex]

[tex] \displaystyle \boxed{x^2 + 5x = 0} [/tex]

3. What do you call an expression that have a polynomial/s in the numerator or denominator?

[tex]\displaystyle \textsf{Rational algebraic expression}[/tex]

4. A rectangular garden has an area of 14m² and a perimeter of 18 meters. find the dimensions of the rectangular garden.

Solution:

[tex] \displaystyle l \cdot w = 14, 2l + 2w = 18 [/tex]

Find l:

[tex] \displaystyle 2l + 2w = 18 [/tex]

[tex] \displaystyle 2l = 18 - 2w [/tex]

[tex] \displaystyle l = 9 - w [/tex]

Replace l with w:

[tex] \displaystyle l \cdot w = 14 [/tex]

[tex] \displaystyle (9 - w) \cdot w = 14 [/tex]

[tex] \displaystyle 9w - w^2 = 14 [/tex]

[tex] \displaystyle 9w - w^2 - 14 = 0 [/tex]

Divide both sides by negative 1:

[tex] \displaystyle -9w + w^2 + 14 = 0 [/tex]

Arrange:

[tex] \displaystyle \boxed{ w^2 - 9w + 14 = 0 } [/tex]

5. The product of two consecutive odd integers is 99. Find the integers.

Solution:

Let [tex] x, x+2 [/tex] be the odd consecutive integers, then:

[tex] \displaystyle x(x+2) = 99 [/tex]

[tex] \displaystyle x^2 + 2x = 99 [/tex]

[tex] \displaystyle x^2 + 2x - 99 = 0 [/tex]

Solve by factoring:

[tex] \displaystyle ( x + 11 )( x - 9) [/tex]

[tex]\displaystyle \boxed{ x = -11, 9 }[/tex]

For the other one:

Let [tex] x, x-2 [/tex] be the odd consecutive integers, then:

[tex] \displaystyle x(x-2) = 99 [/tex]

[tex] \displaystyle x^2 - 2x = 99 [/tex]

[tex] \displaystyle x^2 - 2x - 99 = 0 [/tex]

Solve by factoring:

[tex] \displaystyle ( x - 11 )( x + 9) [/tex]

[tex]\displaystyle \boxed{ x = 11, -9 }[/tex]

6. The product of two consecutive even integers is 168. find the integers.

Solution:

Let [tex] x, x+2 [/tex] be the even consecutive integers, then:

[tex] \displaystyle x(x+2) = 168 [/tex]

[tex] \displaystyle x^2 + 2x = 168 [/tex]

[tex] \displaystyle x^2 + 2x - 168 = 0 [/tex]

Solve by factoring:

[tex] \displaystyle ( x + 12 )( x - 14) [/tex]

[tex]\displaystyle \boxed{ x = -12, 14 }[/tex]

For the other one:

Let [tex] x, x-2 [/tex] be the even consecutive integers, then:

[tex] \displaystyle x(x-2) = 168 [/tex]

[tex] \displaystyle x^2 - 2x = 168 [/tex]

[tex] \displaystyle x^2 - 2x - 168 = 0 [/tex]

Solve by factoring:

[tex] \displaystyle ( x - 12 )( x + 14) [/tex]

[tex]\displaystyle \boxed{ x = 12, -14 }[/tex]

7. Find for the solutions of the equation [tex] x(x - 5) = 36 [/tex]

Solution:

[tex]\displaystyle x (x-5) = 36[/tex]

[tex] \displaystyle x^2 - 5x = 36 [/tex]

[tex] \displaystyle x^2 - 5x - 36 = 0 [/tex]

[tex] \displaystyle ( x + 4 )( x - 9 ) = 0 [/tex]

[tex] \displaystyle \boxed{ x = -4, 9} [/tex]

8. Which of the following equation is an example of a quadratic inequality?

[tex] \displaystyle x^2 - 4x + 4 > 0 [/tex]

9. If the value of x in the quadratic inequality is greater than or greater than or equal to a certain number then the solutions is?

[tex]\displaystyle \textsf{Opposite directions on the number line}[/tex]

10. If the value of x in the quadratic inequality is less than or less than or equal to a certain number then the solutions is?

[tex]\displaystyle \textsf{Toward each other on the number line}[/tex]

Answers:

1. [ Not in the choices ]

2. D

3. A

4. A

5. D

6. B

7. B

8. A

9. C

10. A

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