Given quadratic equation: x² + 2√2x - 6 = 0 Using quadratic formula: x = [-b ± √(b² - 4ac)]/2a Here: a = 1 b = 2√2 c = -6 Substituting: x = [-2√2 ± √(8 - 4(1)(-6))]/2 x = [-2√2 ± √(8 + 24)]/2 x = [-2√2 ± √32]/2 x = [-2√2 ± 4√2]/2 x = [-2√2 ± 4√2]/2 For + sign: x = [-2√2 + 4√2]/2 x = 2√2/2 x = √2 ForRead more
Given quadratic equation: x² + 2√2x – 6 = 0
Using quadratic formula:
x = [-b ± √(b² – 4ac)]/2a
Here:
a = 1
b = 2√2
c = -6
Substituting:
x = [-2√2 ± √(8 – 4(1)(-6))]/2
x = [-2√2 ± √(8 + 24)]/2
x = [-2√2 ± √32]/2
x = [-2√2 ± 4√2]/2
x = [-2√2 ± 4√2]/2
For + sign:
x = [-2√2 + 4√2]/2
x = 2√2/2
x = √2
For – sign:
x = [-2√2 – 4√2]/2
x = -6√2/2
x = -3√2
Given quadratic equation: 2x² - 7x + 3 = 0 For a quadratic equation ax² + bx + c = 0: Sum of roots = -b/a Product of roots = c/a Here: a = 2 b = -7 c = 3 Sum of roots = -(-7)/2 = 7/2 Product of roots = 3/2 To verify: - If we solve for roots using quadratic formula, and add them, we get 7/2 - If we mRead more
Given quadratic equation: 2x² – 7x + 3 = 0
For a quadratic equation ax² + bx + c = 0:
Sum of roots = -b/a
Product of roots = c/a
Here:
a = 2
b = -7
c = 3
Sum of roots = -(-7)/2 = 7/2
Product of roots = 3/2
To verify:
– If we solve for roots using quadratic formula, and add them, we get 7/2
– If we multiply those roots, we get 3/2
Hence, 7/2, 3/2 is the correct answer for sum and product of roots respectively.
For equal roots, discriminant must be zero: b² - 4ac = 0 Given equation: kx² - 6x + 2 = 0 Here: a = k b = -6 c = 2 Putting in discriminant: (-6)² - 4(k)(2) = 0 36 - 8k = 0 8k = 36 k = 9 To check: When k = 9: 9x² - 6x + 2 = 0 Using quadratic formula: x = [6 ± √(36 - 72)]/18 x = [6 ± 0]/18 x = 1/3 (reRead more
For equal roots, discriminant must be zero:
b² – 4ac = 0
Given equation: kx² – 6x + 2 = 0
Here:
a = k
b = -6
c = 2
Putting in discriminant:
(-6)² – 4(k)(2) = 0
36 – 8k = 0
8k = 36
k = 9
To check:
When k = 9:
9x² – 6x + 2 = 0
Using quadratic formula:
x = [6 ± √(36 – 72)]/18
x = [6 ± 0]/18
x = 1/3 (repeated root)
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
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
The roots of the quadratic equation x² + 2√2x – 6 = 0 are:
Given quadratic equation: x² + 2√2x - 6 = 0 Using quadratic formula: x = [-b ± √(b² - 4ac)]/2a Here: a = 1 b = 2√2 c = -6 Substituting: x = [-2√2 ± √(8 - 4(1)(-6))]/2 x = [-2√2 ± √(8 + 24)]/2 x = [-2√2 ± √32]/2 x = [-2√2 ± 4√2]/2 x = [-2√2 ± 4√2]/2 For + sign: x = [-2√2 + 4√2]/2 x = 2√2/2 x = √2 ForRead more
Given quadratic equation: x² + 2√2x – 6 = 0
Using quadratic formula:
x = [-b ± √(b² – 4ac)]/2a
Here:
a = 1
b = 2√2
c = -6
Substituting:
x = [-2√2 ± √(8 – 4(1)(-6))]/2
x = [-2√2 ± √(8 + 24)]/2
x = [-2√2 ± √32]/2
x = [-2√2 ± 4√2]/2
x = [-2√2 ± 4√2]/2
For + sign:
x = [-2√2 + 4√2]/2
x = 2√2/2
x = √2
For – sign:
x = [-2√2 – 4√2]/2
x = -6√2/2
x = -3√2
Therefore, roots are: -3√2 and √2
Hence, -3√2, √2 are the correct roots.
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The sum and product of the roots of the equation 2x² – 7x + 3 = 0 are:
Given quadratic equation: 2x² - 7x + 3 = 0 For a quadratic equation ax² + bx + c = 0: Sum of roots = -b/a Product of roots = c/a Here: a = 2 b = -7 c = 3 Sum of roots = -(-7)/2 = 7/2 Product of roots = 3/2 To verify: - If we solve for roots using quadratic formula, and add them, we get 7/2 - If we mRead more
Given quadratic equation: 2x² – 7x + 3 = 0
For a quadratic equation ax² + bx + c = 0:
Sum of roots = -b/a
Product of roots = c/a
Here:
a = 2
b = -7
c = 3
Sum of roots = -(-7)/2 = 7/2
Product of roots = 3/2
To verify:
– If we solve for roots using quadratic formula, and add them, we get 7/2
– If we multiply those roots, we get 3/2
Hence, 7/2, 3/2 is the correct answer for sum and product of roots respectively.
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If the equation kx² – 6x + 2 = 0 has equal roots, then the value of k is:
For equal roots, discriminant must be zero: b² - 4ac = 0 Given equation: kx² - 6x + 2 = 0 Here: a = k b = -6 c = 2 Putting in discriminant: (-6)² - 4(k)(2) = 0 36 - 8k = 0 8k = 36 k = 9 To check: When k = 9: 9x² - 6x + 2 = 0 Using quadratic formula: x = [6 ± √(36 - 72)]/18 x = [6 ± 0]/18 x = 1/3 (reRead more
For equal roots, discriminant must be zero:
b² – 4ac = 0
Given equation: kx² – 6x + 2 = 0
Here:
a = k
b = -6
c = 2
Putting in discriminant:
(-6)² – 4(k)(2) = 0
36 – 8k = 0
8k = 36
k = 9
To check:
When k = 9:
9x² – 6x + 2 = 0
Using quadratic formula:
x = [6 ± √(36 – 72)]/18
x = [6 ± 0]/18
x = 1/3 (repeated root)
Therefore, 9 is the answer.
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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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See lesshttps://www.tiwariacademy.in/ncert-solutions/class-10/maths/