What is the standard form of the equation \((x+1)(x+2)+(x+3)(x+4)=50\)?
Answer and explanation
Correct answer: \(2x^2+10x-36=0\)
Expanding gives \((x+1)(x+2)=x^2+3x+2\) and \((x+3)(x+4)=x^2+7x+12\). Thus, the left side becomes \(2x^2+10x+14\). Bringing 50 to the left gives \(2x^2+10x+14-50=0\), or \(2x^2+10x-36=0\). Option C is incorrect because dividing the entire equation by 2 would give a constant term of \(-18\), not \(-36\). Exam tip: Write a quadratic equation in standard form as \(ax^2+bx+c=0\).
Frequently asked questions
What is the correct answer to this question?
\(2x^2+10x-36=0\)
Why is this the correct answer?
Expanding gives \((x+1)(x+2)=x^2+3x+2\) and \((x+3)(x+4)=x^2+7x+12\). Thus, the left side becomes \(2x^2+10x+14\). Bringing 50 to the left gives \(2x^2+10x+14-50=0\), or \(2x^2+10x-36=0\). Option C is incorrect because dividing the entire equation by 2 would give a constant term of \(-18\), not \(-36\). Exam tip: Write a quadratic equation in standard form as \(ax^2+bx+c=0\).
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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