Activity 7: Think of These Further!
Direction: Answer the following.
1. Suppose the product of the roots of a quadratic equation is given, do you think you
can determine the equation? Justify your answer.
2. The sum of the roots of the quadratic equation is -5. If one of the roots is 7, how
would you determine the equation? Write the equation.
3. The product of the roots of a quadratic equation is 51. If one of the roots is -17,
what could be the equation?
4. The perimeter of a rectangular bulletin board is 20 ft. If the area of the board is 21
ft²?, what its length and width?
Direction: Answer the following.
1. Suppose the product of the roots of a quadratic equation is given, do you think you
can determine the equation? Justify your answer.
2. The sum of the roots of the quadratic equation is -5. If one of the roots is 7, how
would you determine the equation? Write the equation.
3. The product of the roots of a quadratic equation is 51. If one of the roots is -17,
what could be the equation?
4. The perimeter of a rectangular bulletin board is 20 ft. If the area of the board is 21
ft²?, what its length and width?
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ANSWER
1. If the product of roots is only given, it will be hard since the sum of roots is not given. The clue isnt enough since there are many possibilities using different numbers to find.
2. Sum of roots is -5
Product of roots is 7
Sum is -5
-b/a
-5/1
a= 1 b= 5
Product is 7
c/a
7/1
a= 1 c= 7
GIVEN VALUES
a= 1 b= 5 c= 7
EQUATION: x²+5x+7=0
3. X¹= -17
Product of roots is 51
51 ÷ 17= 3
(x+17)(x+3)
x²+3x+17x+51
EQUATION: x²+20x+51
Sum of roots is -20
4.
P= 2L + 2W
20= 2L + 2W
2
10= L + W
L= 10-w
A= (L)(W)
21= (10-w)(w)
21= 10w-w²
w²-10w+21=0
(w-7)(w-3)
w= 7 & w= 3
CHECKING
AREA
21= (7)(3)
21 = 21
PERIMETER
20= 2(7) + 2(3)
20= 14 + 6
20=20
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