What are the real roots of the equation \(x^2-49=0\)?
Answer and explanation
Correct answer: (7) and (-7)
This is a difference of squares since \(x^2-49=(x-7)(x+7)\). Setting each factor to zero gives roots: from \(x-7=0\) we get \(x=7\), and from \(x+7=0\) we get \(x=-7\). Option B is wrong because using 49 or −49 would imply \(x^2=2401\), which does not satisfy the original equation. Exam tip: when taking square roots remember both signs — from \(x^2=a\) we get \(x=\pm\sqrt{a}\).
Frequently asked questions
What is the correct answer to this question?
(7) and (-7)
Why is this the correct answer?
This is a difference of squares since \(x^2-49=(x-7)(x+7)\). Setting each factor to zero gives roots: from \(x-7=0\) we get \(x=7\), and from \(x+7=0\) we get \(x=-7\). Option B is wrong because using 49 or −49 would imply \(x^2=2401\), which does not satisfy the original equation. Exam tip: when taking square roots remember both signs — from \(x^2=a\) we get \(x=\pm\sqrt{a}\).
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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