Which equation is obtained when \((3x+4)^2=7x+16\) is written in standard quadratic form?
Answer and explanation
Correct answer: \(9x^2+17x=0\)
\((3x+4)^2=9x^2+24x+16\). Therefore, \(9x^2+24x+16=7x+16\). Moving all terms to the left gives \(9x^2+24x+16-7x-16=0\), so \(9x^2+17x=0\). Option B incorrectly treats \(24x-7x\) as \(31x\). Exam tip: write every quadratic equation in the form \(ax^2+bx+c=0\) and combine like terms carefully.
Frequently asked questions
What is the correct answer to this question?
\(9x^2+17x=0\)
Why is this the correct answer?
\((3x+4)^2=9x^2+24x+16\). Therefore, \(9x^2+24x+16=7x+16\). Moving all terms to the left gives \(9x^2+24x+16-7x-16=0\), so \(9x^2+17x=0\). Option B incorrectly treats \(24x-7x\) as \(31x\). Exam tip: write every quadratic equation in the form \(ax^2+bx+c=0\) and combine like terms carefully.
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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