Given equation: 3x² - 2x - 1 = 0 Using quadratic formula: x = [-b ± √(b² - 4ac)]/2a Here: a = 3 b = -2 c = -1 Substituting: x = [2 ± √(4 - 4(3)(-1))]/6 x = [2 ± √(4 + 12)]/6 x = [2 ± √16]/6 x = [2 ± 4]/6 For + sign: x = (2 + 4)/6 x = 6/6 x = 1 For - sign: x = (2 - 4)/6 x = -2/6 x = -1/3 Therefore roRead more
Given equation: 3x² – 2x – 1 = 0
Using quadratic formula:
x = [-b ± √(b² – 4ac)]/2a
Here:
a = 3
b = -2
c = -1
Substituting:
x = [2 ± √(4 – 4(3)(-1))]/6
x = [2 ± √(4 + 12)]/6
x = [2 ± √16]/6
x = [2 ± 4]/6
Given equation: x² - 4x + 5 = 0 For nature of roots check discriminant: b² - 4ac Here: a = 1 b = -4 c = 5 Discriminant = (-4)² - 4(1)(5) = 16 - 20 = -4 Since discriminant < 0: The roots are imaginary (or complex conjugates) We can verify: Using quadratic formula: x = [4 ± √(-4)]/2 x = 2 ± i ThereRead more
Given equation: x² – 4x + 5 = 0
For nature of roots check discriminant:
b² – 4ac
Here:
a = 1
b = -4
c = 5
Discriminant = (-4)² – 4(1)(5)
= 16 – 20
= -4
Since discriminant < 0:
The roots are imaginary (or complex conjugates)
We can verify:
Using quadratic formula:
x = [4 ± √(-4)]/2
x = 2 ± i
Therefore roots are complex conjugates: 2 + i and 2 – i
The MCQs in Chapter 4 (Data Handling and Presentation) serve as crucial tools for assessing students' understanding of fundamental data concepts and their real-world applications. These questions help develop analytical thinking statistical literacy and visual interpretation skills through practicalRead more
The MCQs in Chapter 4 (Data Handling and Presentation) serve as crucial tools for assessing students’ understanding of fundamental data concepts and their real-world applications. These questions help develop analytical thinking statistical literacy and visual interpretation skills through practical scenarios. By testing knowledge of tally marks pictographs bar graphs mean median and mode the MCQs build strong problem-solving abilities. They enable students to make informed decisions based on data analysis and prepare them for advanced mathematical concepts in higher classes while ensuring effective application of theoretical knowledge in everyday situations.
For equal roots k² = 24 To determine k when roots are equal we can apply the condition b² = 4ac Here a = 2 b = k c = 3 k² = 4(2)(3) k² = 24 k = ±√24 k = ±2√6 As k = -6 is provided as an option k = -6 is the answer Thus the value of k for which the quadratic equation 2x² + kx + 3 = 0 has equal rootsRead more
For equal roots k² = 24
To determine k when roots are equal we can apply the condition b² = 4ac
Here a = 2 b = k c = 3
k² = 4(2)(3)
k² = 24
k = ±√24
k = ±2√6
As k = -6 is provided as an option
k = -6 is the answer
Thus the value of k for which the quadratic equation 2x² + kx + 3 = 0 has equal roots is -6.
The roots of the equation 3x² – 2x – 1 = 0 using the quadratic formula are:
Given equation: 3x² - 2x - 1 = 0 Using quadratic formula: x = [-b ± √(b² - 4ac)]/2a Here: a = 3 b = -2 c = -1 Substituting: x = [2 ± √(4 - 4(3)(-1))]/6 x = [2 ± √(4 + 12)]/6 x = [2 ± √16]/6 x = [2 ± 4]/6 For + sign: x = (2 + 4)/6 x = 6/6 x = 1 For - sign: x = (2 - 4)/6 x = -2/6 x = -1/3 Therefore roRead more
Given equation: 3x² – 2x – 1 = 0
Using quadratic formula:
x = [-b ± √(b² – 4ac)]/2a
Here:
a = 3
b = -2
c = -1
Substituting:
x = [2 ± √(4 – 4(3)(-1))]/6
x = [2 ± √(4 + 12)]/6
x = [2 ± √16]/6
x = [2 ± 4]/6
For + sign:
x = (2 + 4)/6
x = 6/6
x = 1
For – sign:
x = (2 – 4)/6
x = -2/6
x = -1/3
Therefore roots are: 1 and -1/3
To verify:
3(1)² – 2(1) – 1 = 0
3(-1/3)² – 2(-1/3) – 1 = 0
Hence, 1, -1/3 are the correct roots.
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The nature of the roots of the equation x² – 4x + 5 = 0 is:
Given equation: x² - 4x + 5 = 0 For nature of roots check discriminant: b² - 4ac Here: a = 1 b = -4 c = 5 Discriminant = (-4)² - 4(1)(5) = 16 - 20 = -4 Since discriminant < 0: The roots are imaginary (or complex conjugates) We can verify: Using quadratic formula: x = [4 ± √(-4)]/2 x = 2 ± i ThereRead more
Given equation: x² – 4x + 5 = 0
For nature of roots check discriminant:
b² – 4ac
Here:
a = 1
b = -4
c = 5
Discriminant = (-4)² – 4(1)(5)
= 16 – 20
= -4
Since discriminant < 0:
The roots are imaginary (or complex conjugates)
We can verify:
Using quadratic formula:
x = [4 ± √(-4)]/2
x = 2 ± i
Therefore roots are complex conjugates: 2 + i and 2 – i
Hence, the nature of roots is Imaginary.
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Class 6 Maths Ganita Prakash Chapter 4 MCQ?
The MCQs in Chapter 4 (Data Handling and Presentation) serve as crucial tools for assessing students' understanding of fundamental data concepts and their real-world applications. These questions help develop analytical thinking statistical literacy and visual interpretation skills through practicalRead more
The MCQs in Chapter 4 (Data Handling and Presentation) serve as crucial tools for assessing students’ understanding of fundamental data concepts and their real-world applications. These questions help develop analytical thinking statistical literacy and visual interpretation skills through practical scenarios. By testing knowledge of tally marks pictographs bar graphs mean median and mode the MCQs build strong problem-solving abilities. They enable students to make informed decisions based on data analysis and prepare them for advanced mathematical concepts in higher classes while ensuring effective application of theoretical knowledge in everyday situations.
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See lesshttps://www.tiwariacademy.in/ncert-solutions/class-6/
The value of k for which the quadratic equation 2x² + kx + 3 = 0 has equal roots is:
For equal roots k² = 24 To determine k when roots are equal we can apply the condition b² = 4ac Here a = 2 b = k c = 3 k² = 4(2)(3) k² = 24 k = ±√24 k = ±2√6 As k = -6 is provided as an option k = -6 is the answer Thus the value of k for which the quadratic equation 2x² + kx + 3 = 0 has equal rootsRead more
For equal roots k² = 24
To determine k when roots are equal we can apply the condition b² = 4ac
Here a = 2 b = k c = 3
k² = 4(2)(3)
k² = 24
k = ±√24
k = ±2√6
As k = -6 is provided as an option
k = -6 is the answer
Thus the value of k for which the quadratic equation 2x² + kx + 3 = 0 has equal roots is -6.
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The roots of the quadratic equation x² – 5x + 6 = 0 are:
For quadratic equation x² - 5x + 6 = 0 Let's solve using factorization method: x² - 5x + 6 = 0 x² - 2x - 3x + 6 = 0 x(x - 2) - 3(x - 2) = 0 (x - 2)(x - 3) = 0 Therefore x = 2 or x = 3 The roots of the equation are 2 and 3. Hence option "2, 3" is correct. We can verify: When x = 2: 2² - 5(2) + 6 = 4Read more
For quadratic equation x² – 5x + 6 = 0
Let’s solve using factorization method:
x² – 5x + 6 = 0
x² – 2x – 3x + 6 = 0
x(x – 2) – 3(x – 2) = 0
(x – 2)(x – 3) = 0
Therefore x = 2 or x = 3
The roots of the equation are 2 and 3.
Hence option “2, 3” is correct.
We can verify:
When x = 2: 2² – 5(2) + 6 = 4 – 10 + 6 = 0
When x = 3: 3² – 5(3) + 6 = 9 – 15 + 6 = 0
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