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If the equation x²- 4x + a=0 has no real roots then the value of a is?
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If the equation x²- 4x + a=0 has no real roots then the value of a is?
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If the equation x²- 4x + a=0 has no real roots then the value of a is?
Understanding the Condition for No Real Roots
For the quadratic equation x² - 4x + a = 0 to have no real roots, we need to analyze the discriminant of the equation. The discriminant (D) is calculated using the formula:
D = b² - 4ac
In this case:
- a = 1 (coefficient of x²)
- b = -4 (coefficient of x)
- c = a (constant term)
Thus, the discriminant becomes:
D = (-4)² - 4(1)(a) = 16 - 4a
Condition for No Real Roots
A quadratic equation has no real roots when the discriminant is less than zero:
D < />
Therefore, we set up the inequality:
16 - 4a < />
Solving the Inequality
Now, we can solve for a:
- Rearranging gives us:
4a > 16
- Dividing both sides by 4:
a > 4
Conclusion
To ensure that the equation x² - 4x + a = 0 has no real roots, the value of a must be greater than 4.
Thus, the final answer is:
- a > 4
This means any value of a that is greater than 4 will result in the quadratic equation having no real roots.
For the quadratic equation x² - 4x + a = 0 to have no real roots, we need to analyze the discriminant of the equation. The discriminant (D) is calculated using the formula:
D = b² - 4ac
In this case:
- a = 1 (coefficient of x²)
- b = -4 (coefficient of x)
- c = a (constant term)
Thus, the discriminant becomes:
D = (-4)² - 4(1)(a) = 16 - 4a
Condition for No Real Roots
A quadratic equation has no real roots when the discriminant is less than zero:
D < />
Therefore, we set up the inequality:
16 - 4a < />
Solving the Inequality
Now, we can solve for a:
- Rearranging gives us:
4a > 16
- Dividing both sides by 4:
a > 4
Conclusion
To ensure that the equation x² - 4x + a = 0 has no real roots, the value of a must be greater than 4.
Thus, the final answer is:
- a > 4
This means any value of a that is greater than 4 will result in the quadratic equation having no real roots.
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If the equation x²- 4x + a=0 has no real roots then the value of a is?
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If the equation x²- 4x + a=0 has no real roots then the value of a is? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If the equation x²- 4x + a=0 has no real roots then the value of a is? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the equation x²- 4x + a=0 has no real roots then the value of a is?.
If the equation x²- 4x + a=0 has no real roots then the value of a is? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If the equation x²- 4x + a=0 has no real roots then the value of a is? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the equation x²- 4x + a=0 has no real roots then the value of a is?.
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