What is the standard form \(ax^2+bx+c=0\) of the equation \((x+2)^2+2(x-3)^2=35\)?
Answer and explanation
Correct answer: \(3x^2-8x-13=0\)
Expand the squares: \((x+2)^2=x^2+4x+4\) and \(2(x-3)^2=2x^2-12x+18\). Thus, \(3x^2-8x+22=35\), and moving 35 to the left gives \(3x^2-8x-13=0\). Therefore, option A is correct. Exam tip: when converting to standard form, keep all terms on one side and make the other side zero; the constant becomes \(22-35=-13\).
Frequently asked questions
What is the correct answer to this question?
\(3x^2-8x-13=0\)
Why is this the correct answer?
Expand the squares: \((x+2)^2=x^2+4x+4\) and \(2(x-3)^2=2x^2-12x+18\). Thus, \(3x^2-8x+22=35\), and moving 35 to the left gives \(3x^2-8x-13=0\). Therefore, option A is correct. Exam tip: when converting to standard form, keep all terms on one side and make the other side zero; the constant becomes \(22-35=-13\).
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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