What is the standard quadratic form of \((3x+2)(x-5)=0\)?
Answer and explanation
Correct answer: \(3x^2-13x-10=0\)
Expanding \((3x+2)(x-5)\) gives \(3x^2-15x+2x-10\). Combining like terms \(-15x+2x=-13x\) yields the standard form \(3x^2-13x-10=0\). Option C shows an intermediate grouping without combining the like x-terms; options B and D have incorrect signs or constants. Exam tip: always expand first, then combine like terms and write coefficients in descending powers of x.
Frequently asked questions
What is the correct answer to this question?
\(3x^2-13x-10=0\)
Why is this the correct answer?
Expanding \((3x+2)(x-5)\) gives \(3x^2-15x+2x-10\). Combining like terms \(-15x+2x=-13x\) yields the standard form \(3x^2-13x-10=0\). Option C shows an intermediate grouping without combining the like x-terms; options B and D have incorrect signs or constants. Exam tip: always expand first, then combine like terms and write coefficients in descending powers of x.
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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