Algebra Ex 3.11-10th Std Maths-Book Back Question And Answer
Completing the Square Calculator is an online tool that helps to complete the square of a quadratic equation and calculate its roots.
Question 1.
Solve the following quadratic equations by completing the square method
(i) 9x2 – 12x + 4 = 0
Answer:
9x2 – 12x + 4 = 0
x2 – 12x9 + 49 = 0 (Divided by 9)
x2 – 4x3 = −49
Add [12 (43)]2 on both sides
The solution is 23
(ii) 5x+7x−1 = 3x + 2
Answer:
(3x + 2) (x – 1) = 5x + 7
3x2 – 3x + 2x – 2 = 5x + 7 ⇒ 3x2 – x – 5x – 2 – 7 = 0
3x2 – 6x – 9 = 0 ⇒ x2 – 2x – 3 = 0 (divided by 3)
x2 – 2x = 3
Adding (12 × 2)2 on both sides
x2 – 2x + 1 = 3 + 1
(x – 1)2 = 4 ⇒ x – 1 = 4–√
x – 1 = ±2
x – 1 = 2 or x – 1 = -2
x = 3 or x = -1
The solution set is -1 and 3
Question 2.
Solve the following quadratic equations by formula method
(i) 2x2 – 5x + 2 = 0
Answer:
a = 2, b = -5, c = 2
The solution set is 12 and 2
(ii) 2–√ f2 – 6 f + 3 2–√ = 0
Answer:
Here a = 2–√, b = -6 and c = 32–√
The solution set is 3+3√2√ and 3−3√2√
(iii) 3y2 – 20y – 23 = 0
Answer:
a = 3, b = -20, c = -23
The solution set is -1 and 233
(iv) 36y2 – 12ay + (a2 – b2) = 0
Answer
Here a = 36, b = -12a, c = a2 – b2
The solution set is (a+b)6 and (a−b)6
Question 3.
A ball rolls down a slope and travels a distance d = t2 – 0.75t feet in t seconds. Find the time when the distance travelled by the ball is 11.25 feet.
Answer:
Distance = t2 – 0.75t
11.25 = t2 – 0.75t
Multiply by 100
1125 = 100t2 – 75t
100t2 – 75t – 1125 = 0 (Divided by 25)
4t2 – 3t – 45 = 0
a = 4,
b = -3,
c = -45
(time will not be negative)
The required time = 154 seconds
= 3 34 second or 3.75 seconds
