A root is of an equation is a number which can be put in place of variable can be x or any other variable, and after solving the equation we check if Left hand side is equal to right hand side means in place of variable you have to put the number and check if the left hand side is equal to right hand side then the number is root for particular equation otherwise it’s not the root.
App ko variable jo ki x, y ,z kuch bhi ho sakta hi us jagah pe jo numeric value di hi use put karke solve kare aur yadi Left hand side aur right hand side same ate hi to wo us equation ka root hi nahi to nahi hi.
Q1 . Determine by substitution IF
a. Is 3 the root of 8x = 24?
Substitute (Replace x with 3): 8 X 3 = 24
8 X 3 is 24.
24 = 24.
Answer: 3 is a root.
So 3 is the root of the Above equation.
b. Is 4 the root of 2x – 3 = 5?
Substitute: (2 X 4) – 3 = 5
8 – 3 = 5.
5 = 5.
Answer: 4 is a root of the above equation.
c. Is -3 the root of x + 12 = 9?
Substitute: (-3) + 12 = 9
Calculate: -3 + 12 = 9.
9 = 9.
Answer: -3 is a root of the above equation.
d. Is -3 the root of 2(x + 4) = 14?
Substitute: 2 x (-3 + 4) = 14
Calculate inside ( ) first: -3 + 4 = 1.
Now multiply: 2 x 1 = 2.
2 is not equal to 14.
Answer: -3 is not a root of the above question.
e. Is 3 the root of (x+1)/2 + (x-1)/2 = 3?
Substitute: (3+1)/2 + (3-1)/2 = 3
Calculate: (4)/2 + (2)/2 = 3 → 2 + 1 = 3
3 = 3.
Answer: 3 is a root of the above equation
f. Is -1 the root of -2x + 1 = 0?
Substitute: (-2 x -1) + 1 = 0
Calculate: (-2 x -1) is +2. So, 2 + 1 = 3.
3 is not equal to 0.
Answer: -1 is not a root of above equation
g. Is 5 the root of (x – 3)(x – 2) = 6?
Substitute: (5 – 3) x (5 – 2) = 6
Calculate: (2) x (3) = 6.
6 = 6.
Answer: Yes, 5 is a root.
Q2 . Which of the following numbers satisfy the given equations?
- X+3 = 9; options 5,3, – 3, 6
Try 5: 5 + 3 = 8.
8 ≠ 9
Try 3: 3 + 3 = 6.
6 ≠ 9.
Try -3: -3 + 3 = 0.
0 ≠ 9.
Try 6: 6 + 3 = 9.
9 = 9.
Answer: 6
(b) Equation: 7 – x = 3. Options: 7, -4, 4, 5
Try 7: 7 – 7 = 0.
0 ≠ 3.
Try -4: 7 – (-4) = 7 + 4 = 11.
11 ≠ 3.
Try 4: 7 – 4 = 3.
3 = 3.
Try 5: 7 – 5 = 2.
2 ≠ 3.
Answer: 4
c. Equation: 4 + y = -2. Options: 2, -2, 0, -6, 6
Try 2: 4 + 2 = 6.
6 ≠ -2.
Try -2: 4 + (-2) = 2.
2 ≠ -2.
Try 0: 4 + 0 = 4.
4 ≠ -2.
Try -6: 4 + (-6) = -2.
-2 = -2.
Try 6: 4 + 6 = 10.
10 ≠ -2.
Answer: -6
d. Equation: -6 + z = -8. Options: 2, +2, -2, 4
Try 2: -6 + 2 = -4.
-4 ≠ -8.
Try +2: -6 +2
-4 ≠ -8.
Try -2: -6 + (-2) =
-8. -8 = -8.
Try 4: -6 + 4 = -2.
-2 ≠ -8.
- Answer: -2
e. Equation: 2x = 16. Options: -8, 2, 8, 0
Try -8: 2 X (-8) = -16.
-16 ≠ 16.
Try 2: 2 X 2 = 4.
4 ≠ 16.
Try 8: 2 X 8 = 16.
16 = 16.
Try 0: 2 X 0 = 0.
0 ≠ 16.
Answer: 8
f. Equation: y/2 = 6. Options: 6, 3, 4, 12, 0
Try 6: 6 / 2 = 3.
3 ≠ 6.
Try 3: 3 / 2 = 1.5.
1.5 ≠ 6.
Try 4: 4 / 2 = 2.
2 ≠ 6.
Try 12: 12 / 2 = 6.
6 = 6.
Try 0: 0 / 2 = 0.
0 ≠ 6.
Answer: 12
g. Equation: (x+1)/3 = 7. Options: 16, 21, 20, -20
Try 16: (16 + 1) / 3 = 17 / 3 = 5.66.
5.66 ≠ 7.
Try 21: (21 + 1) / 3 = 22 / 3 = 7.33.
7.33 ≠ 7.
Try 20: (20 + 1) / 3 = 21 / 3 = 7.
7 = 7.
Try -20: (-20 + 1) / 3 = (-19)/3 = -6.33.
-6.33 ≠ 7.
Answer: 20
h. Equation: x + 6 = 9. Options: 9, 3, 0, 9, -3
Try 9: 9 + 6 = 15.
15 ≠ 9.
Try 3: 3 + 6 = 9.
9 = 9.
Try 0: 0 + 6 = 6.
6 ≠ 9.
Try 9: (9+6 ) = 15
15 ≠ 9.
Try -3: -3 + 6 = 3.
3 ≠ 9.
Answer: 3