What is the root of x² − 2√5x + 5 = 0?
Answer and explanation
Correct answer: x = √5
The governing concept is solving a quadratic equation by recognizing a perfect square. Compare x² − 2√5x + 5 with the identity (x − c)² = x² − 2cx + c². Taking c = √5 gives c² = 5, so the equation becomes x² − 2√5x + 5 = (x − √5)² = 0. A square can equal zero only when its base is zero; hence x − √5 = 0 and x = √5. The root is repeated because both quadratic roots coincide. Therefore option A is correct. Option B has the wrong sign, while C and D confuse the constant 5 with the root and do not satisfy the equation.
Frequently asked questions
What is the correct answer to this question?
x = √5
Why is this the correct answer?
The governing concept is solving a quadratic equation by recognizing a perfect square. Compare x² − 2√5x + 5 with the identity (x − c)² = x² − 2cx + c². Taking c = √5 gives c² = 5, so the equation becomes x² − 2√5x + 5 = (x − √5)² = 0. A square can equal zero only when its base is zero; hence x − √5 = 0 and x = √5. The root is repeated because both quadratic roots coincide. Therefore option A is correct. Option B has the wrong sign, while C and D confuse the constant 5 with the root and do not satisfy the equation.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Methods of Solving Quadratic Equations.
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