When the equation (x-2)^2+(2x+1)^2=25 is written in the standard quadratic form ax^2+bx+c=0, which form is obtained?
Answer and explanation
Correct answer: \(5x^2-20=0\)
Expanding gives \((x-2)^2=x^2-4x+4\) and \((2x+1)^2=4x^2+4x+1\). Therefore, \(5x^2+5=25\); moving 25 to the left gives \(5x^2-20=0\). Hence, option D is correct. Exam tip: To obtain standard form, bring all terms to one side and set the resulting expression equal to zero.
Frequently asked questions
What is the correct answer to this question?
\(5x^2-20=0\)
Why is this the correct answer?
Expanding gives \((x-2)^2=x^2-4x+4\) and \((2x+1)^2=4x^2+4x+1\). Therefore, \(5x^2+5=25\); moving 25 to the left gives \(5x^2-20=0\). Hence, option D is correct. Exam tip: To obtain standard form, bring all terms to one side and set the resulting expression equal to zero.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Introduction to Quadratic Equations.
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