Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.11

Students can download Maths Chapter 3 Algebra Ex 3.11 Questions and Answers, Notes, Samacheer Kalvi 10th Maths Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 3 Algebra Ex 3.11

Question 1.
Solve the following quadratic equations by completing the square method
(i) 9x2 – 12x + 4 = 0
Answer:
9x2 – 12x + 4 = 0
x2 – \(\frac { 12x }{ 9 } \) + \(\frac { 4 }{ 9 } \) = 0 (Divided by 9)
x2 – \(\frac { 4x }{ 3 } \) = \(\frac { -4 }{ 9 } \)
Add [\(\frac { 1 }{ 2 } \) (\(\frac { 4 }{ 3 } \))]2 on both sides
Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.11 1
The solution is \(\frac { 2 }{ 3 } \)

Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.11

(ii) \(\frac { 5x+7 }{ x-1 } \) = 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 (\(\frac { 1 }{ 2 } \) × 2)2 on both sides
x2 – 2x + 1 = 3 + 1
(x – 1)2 = 4 ⇒ x – 1 = \(\sqrt { 4 }\)
x – 1 = ±2
x – 1 = 2 or x – 1 = -2
x = 3 or x = -1
The solution set is -1 and 3

Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.11

Question 2.
Solve the following quadratic equations by formula method
(i) 2x2 – 5x + 2 = 0
Answer:
a = 2, b = -5, c = 2
Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.11 2
The solution set is \(\frac { 1 }{ 2 } \) and 2

(ii) \(\sqrt { 2 }\) f2 – 6 f + 3 \(\sqrt { 2 }\) = 0
Answer:
Here a = \(\sqrt { 2 }\), b = -6 and c = 3\(\sqrt { 2 }\)
Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.11 3
The solution set is \(\frac{3+\sqrt{3}}{\sqrt{2}}\) and \(\frac{3-\sqrt{3}}{\sqrt{2}}\)

(iii) 3y2 – 20y – 23 = 0
Answer:
a = 3, b = -20, c = -23
Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.11 4
The solution set is -1 and \(\frac { 23 }{ 3 } \)

(iv) 36y2 – 12ay + (a2 – b2) = 0
Answer:
Here a = 36, b = -12a, c = a2 – b2
Samacheer Kalvi 10th <img class=
The solution set is \(\frac { (a+b) }{ 6 } \) and \(\frac { (a-b) }{ 6 } \)

Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.11

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
Samacheer Kalvi 10th Maths Guide Chapter 3 Algebra Ex 3.11 7
(time will not be negative)
The required time = \(\frac { 15 }{ 4 } \) seconds
= 3 \(\frac { 3 }{ 4 } \) second or 3.75 seconds

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