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The roots of the equation x2 – 8x + 16 = 0
- a)are imaginary
- b)are distinct and real
- c)are equal and real
- d)Cannot be determined
Correct answer is option 'C'. Can you explain this answer?
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Roots of the Equation x^2 - 8x + 16 = 0
To determine the nature of the roots of the given equation x^2 - 8x + 16 = 0, we need to analyze the discriminant of the quadratic equation.
Discriminant of the Quadratic Equation
The discriminant of a quadratic equation in the form ax^2 + bx + c = 0 is given by the expression b^2 - 4ac. For the given equation x^2 - 8x + 16 = 0, the values of a, b, and c are 1, -8, and 16 respectively.
Calculating the Discriminant
In this case, the discriminant can be calculated as follows:
b^2 - 4ac = (-8)^2 - 4(1)(16) = 64 - 64 = 0
Interpreting the Discriminant
When the discriminant of a quadratic equation is equal to zero, it implies that the equation has equal and real roots. In other words, the equation has one real root repeated twice.
Therefore, in the given equation x^2 - 8x + 16 = 0, the roots are equal and real.
This explanation helps in understanding the concept of discriminant and how it can be used to determine the nature of roots of a quadratic equation.
To determine the nature of the roots of the given equation x^2 - 8x + 16 = 0, we need to analyze the discriminant of the quadratic equation.
Discriminant of the Quadratic Equation
The discriminant of a quadratic equation in the form ax^2 + bx + c = 0 is given by the expression b^2 - 4ac. For the given equation x^2 - 8x + 16 = 0, the values of a, b, and c are 1, -8, and 16 respectively.
Calculating the Discriminant
In this case, the discriminant can be calculated as follows:
b^2 - 4ac = (-8)^2 - 4(1)(16) = 64 - 64 = 0
Interpreting the Discriminant
When the discriminant of a quadratic equation is equal to zero, it implies that the equation has equal and real roots. In other words, the equation has one real root repeated twice.
Therefore, in the given equation x^2 - 8x + 16 = 0, the roots are equal and real.
This explanation helps in understanding the concept of discriminant and how it can be used to determine the nature of roots of a quadratic equation.
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The roots of the equation x2 8x + 16 = 0a)are imaginaryb)are distinct and realc)are equal and reald)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer?
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The roots of the equation x2 8x + 16 = 0a)are imaginaryb)are distinct and realc)are equal and reald)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about The roots of the equation x2 8x + 16 = 0a)are imaginaryb)are distinct and realc)are equal and reald)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The roots of the equation x2 8x + 16 = 0a)are imaginaryb)are distinct and realc)are equal and reald)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer?.
The roots of the equation x2 8x + 16 = 0a)are imaginaryb)are distinct and realc)are equal and reald)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about The roots of the equation x2 8x + 16 = 0a)are imaginaryb)are distinct and realc)are equal and reald)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The roots of the equation x2 8x + 16 = 0a)are imaginaryb)are distinct and realc)are equal and reald)Cannot be determinedCorrect answer is option 'C'. Can you explain this answer?.
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