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The quadratic equation whose roots are 5 and -2 is:
The quadratic equation whose roots are 5 and -2 is: x² - 3x - 10 = 0 Let's verify: If α = 5 and β = -2 are roots then: Sum of roots = -(coefficient of x)/coefficient of x² α + β = -b/a = 3 Product of roots = constant term/coefficient of x² α × β = c/a = -10 Therefore x² - 3x - 10 = 0 is correct as:Read more
The quadratic equation whose roots are 5 and -2 is: x² – 3x – 10 = 0
Let’s verify:
If α = 5 and β = -2 are roots then:
Sum of roots = -(coefficient of x)/coefficient of x²
α + β = -b/a = 3
Product of roots = constant term/coefficient of x²
α × β = c/a = -10
Therefore x² – 3x – 10 = 0 is correct as:
– coefficient of x: -(α + β) = -3
– constant term: α × β = -10
Hence option x² – 3x – 10 = 0 is correct.
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If one root of the equation x² + px + 12 = 0 is -3, then the value of p is:
Given equation: x² + px + 12 = 0 One root is -3 Since -3 is a root it must satisfy the equation: (-3)² + p(-3) + 12 = 0 Simplifying: 9 - 3p + 12 = 0 21 - 3p = 0 -3p = -21 p = 7 To verify: When p = 7: x² + 7x + 12 = 0 Roots are -3 and -4 One root is indeed -3 Hence, 7 is the correct answer. Click herRead more
Given equation: x² + px + 12 = 0
One root is -3
Since -3 is a root it must satisfy the equation:
(-3)² + p(-3) + 12 = 0
Simplifying:
9 – 3p + 12 = 0
21 – 3p = 0
-3p = -21
p = 7
To verify:
When p = 7:
x² + 7x + 12 = 0
Roots are -3 and -4
One root is indeed -3
Hence, 7 is the correct answer.
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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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