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If the roots of x^2-2mx m^2-1=0 between -2 and 4,then
1. -3 less than or equal to 3
2. -2 less than or equal to 5
3. -1 less than or equal to 5
4. -1 less than or equal to 3?
1. -3 less than or equal to 3
2. -2 less than or equal to 5
3. -1 less than or equal to 5
4. -1 less than or equal to 3?
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If the roots of x^2-2mx m^2-1=0 between -2 and 4,then 1. -3 less than ...
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If the roots of x^2-2mx m^2-1=0 between -2 and 4,then 1. -3 less than ...
To find the range of values for m that satisfy the given conditions, we need to consider the range of the roots of the quadratic equation x^2 - 2mx + (m^2 - 1) = 0 within the interval [-2, 4].
1. -3 ≤ m ≤ 3:
If the roots of the quadratic equation lie between -2 and 4, we can write the condition as -2 < r1="" />< r2="" />< 4,="" where="" r1="" and="" r2="" are="" the="" roots="" of="" the="" />
Let's find the discriminant of the quadratic equation: D = b^2 - 4ac.
In this case, a = 1, b = -2m, and c = m^2 - 1.
D = (-2m)^2 - 4(1)(m^2 - 1)
D = 4m^2 - 4m^2 + 4
D = 4
Since the discriminant is positive, the roots are real and distinct.
The sum of the roots is given by: r1 + r2 = -b/a = 2m/1 = 2m.
The product of the roots is given by: r1 * r2 = c/a = (m^2 - 1)/1 = m^2 - 1.
From the condition -2 < r1="" />< r2="" />< 4,="" we="" have="" -2="" />< r1="" +="" r2="" />< />
Substituting the values, we get -2 < 2m="" />< />
Dividing the inequality by 2, we have -1 < m="" />< />
Therefore, the range of m that satisfies this condition is -1 < m="" />< />
2. -2 ≤ m ≤ 5:
Using the same approach as above, the sum of the roots is: r1 + r2 = 2m, and the product of the roots is: r1 * r2 = m^2 - 1.
From the condition -2 < r1="" />< r2="" />< 4,="" we="" have="" -2="" />< 2m="" />< />
Dividing the inequality by 2, we have -1 < m="" />< />
Therefore, the range of m that satisfies this condition is -1 < m="" />< />
3. -1 ≤ m ≤ 5:
Again, the sum of the roots is: r1 + r2 = 2m, and the product of the roots is: r1 * r2 = m^2 - 1.
From the condition -2 < r1="" />< r2="" />< 4,="" we="" have="" -2="" />< 2m="" />< />
Dividing the inequality by 2, we have -1 < m="" />< />
Therefore, the range of m that satisfies this condition is -1 < m="" />< />
4. -1 ≤ m ≤ 3:
Using the same approach as above, the sum of the roots is: r1 + r2 = 2m, and the product of the roots is: r1 * r2 = m^2 - 1.
From the condition -2 < r1="" />< r2="" />< 4,="" we="" have="" -2="" />< 2m="" />< />
Dividing the inequality by 2, we have -1 < m="" />< />
Therefore, the range of m
1. -3 ≤ m ≤ 3:
If the roots of the quadratic equation lie between -2 and 4, we can write the condition as -2 < r1="" />< r2="" />< 4,="" where="" r1="" and="" r2="" are="" the="" roots="" of="" the="" />
Let's find the discriminant of the quadratic equation: D = b^2 - 4ac.
In this case, a = 1, b = -2m, and c = m^2 - 1.
D = (-2m)^2 - 4(1)(m^2 - 1)
D = 4m^2 - 4m^2 + 4
D = 4
Since the discriminant is positive, the roots are real and distinct.
The sum of the roots is given by: r1 + r2 = -b/a = 2m/1 = 2m.
The product of the roots is given by: r1 * r2 = c/a = (m^2 - 1)/1 = m^2 - 1.
From the condition -2 < r1="" />< r2="" />< 4,="" we="" have="" -2="" />< r1="" +="" r2="" />< />
Substituting the values, we get -2 < 2m="" />< />
Dividing the inequality by 2, we have -1 < m="" />< />
Therefore, the range of m that satisfies this condition is -1 < m="" />< />
2. -2 ≤ m ≤ 5:
Using the same approach as above, the sum of the roots is: r1 + r2 = 2m, and the product of the roots is: r1 * r2 = m^2 - 1.
From the condition -2 < r1="" />< r2="" />< 4,="" we="" have="" -2="" />< 2m="" />< />
Dividing the inequality by 2, we have -1 < m="" />< />
Therefore, the range of m that satisfies this condition is -1 < m="" />< />
3. -1 ≤ m ≤ 5:
Again, the sum of the roots is: r1 + r2 = 2m, and the product of the roots is: r1 * r2 = m^2 - 1.
From the condition -2 < r1="" />< r2="" />< 4,="" we="" have="" -2="" />< 2m="" />< />
Dividing the inequality by 2, we have -1 < m="" />< />
Therefore, the range of m that satisfies this condition is -1 < m="" />< />
4. -1 ≤ m ≤ 3:
Using the same approach as above, the sum of the roots is: r1 + r2 = 2m, and the product of the roots is: r1 * r2 = m^2 - 1.
From the condition -2 < r1="" />< r2="" />< 4,="" we="" have="" -2="" />< 2m="" />< />
Dividing the inequality by 2, we have -1 < m="" />< />
Therefore, the range of m
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If the roots of x^2-2mx m^2-1=0 between -2 and 4,then 1. -3 less than or equal to 3 2. -2 less than or equal to 5 3. -1 less than or equal to 5 4. -1 less than or equal to 3?
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If the roots of x^2-2mx m^2-1=0 between -2 and 4,then 1. -3 less than or equal to 3 2. -2 less than or equal to 5 3. -1 less than or equal to 5 4. -1 less than or equal to 3? for Class 12 2025 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about If the roots of x^2-2mx m^2-1=0 between -2 and 4,then 1. -3 less than or equal to 3 2. -2 less than or equal to 5 3. -1 less than or equal to 5 4. -1 less than or equal to 3? covers all topics & solutions for Class 12 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the roots of x^2-2mx m^2-1=0 between -2 and 4,then 1. -3 less than or equal to 3 2. -2 less than or equal to 5 3. -1 less than or equal to 5 4. -1 less than or equal to 3?.
If the roots of x^2-2mx m^2-1=0 between -2 and 4,then 1. -3 less than or equal to 3 2. -2 less than or equal to 5 3. -1 less than or equal to 5 4. -1 less than or equal to 3? for Class 12 2025 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about If the roots of x^2-2mx m^2-1=0 between -2 and 4,then 1. -3 less than or equal to 3 2. -2 less than or equal to 5 3. -1 less than or equal to 5 4. -1 less than or equal to 3? covers all topics & solutions for Class 12 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the roots of x^2-2mx m^2-1=0 between -2 and 4,then 1. -3 less than or equal to 3 2. -2 less than or equal to 5 3. -1 less than or equal to 5 4. -1 less than or equal to 3?.
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