What is the repeated root of the equation \(x^2-8x+16=0\)?
Answer and explanation
Correct answer: 4
Factor the quadratic: \(x^2-8x+16=(x-4)^2\). Hence \((x-4)^2=0\) gives the repeated root \(x=4\). Alternatively compute the discriminant: \(\Delta=b^2-4ac=(-8)^2-4\cdot1\cdot16=0\), and \(\Delta=0\) indicates a double root. The closest distractor \(-4\) is incorrect because substituting \(-4\) does not satisfy the equation (it gives 64). Exam tip: either factor into a perfect square or check the discriminant; if \(\Delta=0\) the root is repeated.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
Factor the quadratic: \(x^2-8x+16=(x-4)^2\). Hence \((x-4)^2=0\) gives the repeated root \(x=4\). Alternatively compute the discriminant: \(\Delta=b^2-4ac=(-8)^2-4\cdot1\cdot16=0\), and \(\Delta=0\) indicates a double root. The closest distractor \(-4\) is incorrect because substituting \(-4\) does not satisfy the equation (it gives 64). Exam tip: either factor into a perfect square or check the discriminant; if \(\Delta=0\) the root is repeated.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.
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