:Determine the NATURE OF THE ROOTS of the following quadratic equations using the DISCRIMINANT,SUM and PRODUCT.
-DISCRIMINANT
-NATURE OF THE ROOTS
-SUM
-PRODUCT
1. x² + 6x + 9 =0
2. x² + 9x + 20 =0
3. 2x² - 10x + 8 =0
4. x² + 5x + 10 =0
5. x² + 6x + 3 =0
6. 2x² + 6x + 4 =0
7. 3x² - 5x = -4
8. 9x² - 6x = -9
9. 10x² - 4x = 8
10. 3x² - 2x - 5 =0
-DISCRIMINANT
-NATURE OF THE ROOTS
-SUM
-PRODUCT
1. x² + 6x + 9 =0
2. x² + 9x + 20 =0
3. 2x² - 10x + 8 =0
4. x² + 5x + 10 =0
5. x² + 6x + 3 =0
6. 2x² + 6x + 4 =0
7. 3x² - 5x = -4
8. 9x² - 6x = -9
9. 10x² - 4x = 8
10. 3x² - 2x - 5 =0
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Determine the NATURE OF THE ROOTS of the following quadratic equations using the DISCRIMINANT,SUM and PRODUCT.
1. x² + 6x + 9 =0
VALUES OF A, B, & C: a= 1, b= 6, c= 9
DISCRIMINANT:
b²-4ac
(6)²-4(1)(9)
36-36= 0
NATURE OF THE ROOTS: Real, rational and equal
SUM:
-b/a
-6/1 = -6
PRODUCT:
c/a
9/1= 9
2. x² + 9x + 20 =0
VALUES OF A, B, & C: a= 1, b= 9, c= 20
DISCRIMINANT:
b²-4ac
(9)²-4(1)(20)
81-80= 1
NATURE OF THE ROOTS: Real, rational and unequal
SUM:
-b/a
-9/1 = -9
PRODUCT:
c/a
20/1= 20
3. 2x² - 10x + 8 =0
VALUES OF A, B, & C: a= 2, b= -10, c= 8
DISCRIMINANT:
b²-4ac
(-10)²-4(2)(8)
100-64= 36
NATURE OF THE ROOTS: Real, rational and unequal
SUM:
-b/a
-(-10)/2
10/2= 5
PRODUCT:
c/a
8/2= 4
4. x² + 5x + 10 =0
VALUES OF A, B, & C: a= 1, b= 5, c= 10
DISCRIMINANT:
b²-4ac
(5)²-4(1)(10)
25-40= -15
NATURE OF THE ROOTS: Not real
SUM:
-b/a
-5/1 = -5
PRODUCT:
c/a
10/1= 10
5. x² + 6x + 3 =0
VALUES OF A, B, & C: a= 1, b= 6, c= 3
DISCRIMINANT:
b²-4ac
(6)²-4(1)(3)
36-12= 24
NATURE OF THE ROOTS: Real, irrational and unequal
SUM:
-b/a
-6/1= -6
PRODUCT:
c/a
3/1= 3
6. 2x² + 6x + 4 =0
VALUES OF A, B, & C: a= 2, b= 6, c= 4
DISCRIMINANT:
b²-4ac
(6)²-4(2)(4)
36-32= 4
NATURE OF THE ROOTS: Real, rational and unequal
SUM:
-b/a
-6/2= -3
PRODUCT:
c/a
4/2= 2
7. 3x² - 5x = -4
VALUES OF A, B, & C: a= 3, b= -5, c= -4
DISCRIMINANT:
b²-4ac
(-5)²-4(3)(-4)
25+48= 73
NATURE OF THE ROOTS: Real, irrational and unequal
SUM:
-b/a
-(-5)/3
5/3
PRODUCT:
c/a
-4/3
8. 9x² - 6x = -9
VALUES OF A, B, & C: a= 9, b= -6, c= -9
DISCRIMINANT:
b²-4ac
(-6)²-4(9)(-9)
36+324= 360
NATURE OF THE ROOTS: Real, irrational and unequal
SUM:
-b/a
-(-6)/9
6/9= 2/3
PRODUCT:
c/a
-9/9= -1
9. 10x² - 4x = 8
VALUES OF A, B, & C: a= 10, b= -4, c= -8
DISCRIMINANT:
b²-4ac
(-4)²-4(10)(-8)
16+320= 336
NATURE OF THE ROOTS: Real, irrational and unequal
SUM:
-b/a
-(-4)/10
4/10= 2/5
PRODUCT:
c/a
-8/10= -4/5
10. 3x² - 2x - 5 =0
VALUES OF A, B, & C: a= 3, b= -2, c= -5
DISCRIMINANT:
b²-4ac
(-2)²-4(3)(-5)
4+60= 64
NATURE OF THE ROOTS: Real, rational and unequal
SUM:
-b/a
-(-2)/3
2/3
PRODUCT:
c/a
-5/3