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Find the value of k for which the roots of quadratic equation 5x² - 10 X + 10 is equals to zero a real and equal?
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Find the value of k for which the roots of quadratic equation 5x² - 10...
Understanding the Quadratic Equation
The quadratic equation given is:
5x² - 10x + 10 = 0
For this equation to have real and equal roots, the discriminant must be zero.
What is the Discriminant?
The discriminant (D) of a quadratic equation ax² + bx + c is given by the formula:
D = b² - 4ac
Here, a = 5, b = -10, and c = 10.
Calculating the Discriminant
Let's substitute the values into the discriminant formula:
- **b²** = (-10)² = 100
- **4ac** = 4 × 5 × 10 = 200
Now, calculate D:
D = 100 - 200 = -100
Since D < 0,="" the="" equation="" currently="" has="" no="" real="" />
Condition for Real and Equal Roots
To ensure the roots are real and equal, we need D = 0. Thus, we need to adjust the value of c in our equation.
Setting the Discriminant to Zero
We can set the discriminant to zero:
0 = b² - 4ac
Substituting our values:
0 = (-10)² - 4 × 5 × c
This simplifies to:
0 = 100 - 20c
Now, solve for c:
20c = 100
c = 5
Final Quadratic Equation
Thus, for the quadratic equation 5x² - 10x + 5 = 0, the roots will be real and equal.
In conclusion, the value of k for which the roots of the quadratic equation become real and equal is **5**.
The quadratic equation given is:
5x² - 10x + 10 = 0
For this equation to have real and equal roots, the discriminant must be zero.
What is the Discriminant?
The discriminant (D) of a quadratic equation ax² + bx + c is given by the formula:
D = b² - 4ac
Here, a = 5, b = -10, and c = 10.
Calculating the Discriminant
Let's substitute the values into the discriminant formula:
- **b²** = (-10)² = 100
- **4ac** = 4 × 5 × 10 = 200
Now, calculate D:
D = 100 - 200 = -100
Since D < 0,="" the="" equation="" currently="" has="" no="" real="" />
Condition for Real and Equal Roots
To ensure the roots are real and equal, we need D = 0. Thus, we need to adjust the value of c in our equation.
Setting the Discriminant to Zero
We can set the discriminant to zero:
0 = b² - 4ac
Substituting our values:
0 = (-10)² - 4 × 5 × c
This simplifies to:
0 = 100 - 20c
Now, solve for c:
20c = 100
c = 5
Final Quadratic Equation
Thus, for the quadratic equation 5x² - 10x + 5 = 0, the roots will be real and equal.
In conclusion, the value of k for which the roots of the quadratic equation become real and equal is **5**.
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Find the value of k for which the roots of quadratic equation 5x² - 10 X + 10 is equals to zero a real and equal?
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Find the value of k for which the roots of quadratic equation 5x² - 10 X + 10 is equals to zero a real and equal? 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 Find the value of k for which the roots of quadratic equation 5x² - 10 X + 10 is equals to zero a real and equal? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the value of k for which the roots of quadratic equation 5x² - 10 X + 10 is equals to zero a real and equal?.
Find the value of k for which the roots of quadratic equation 5x² - 10 X + 10 is equals to zero a real and equal? 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 Find the value of k for which the roots of quadratic equation 5x² - 10 X + 10 is equals to zero a real and equal? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the value of k for which the roots of quadratic equation 5x² - 10 X + 10 is equals to zero a real and equal?.
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