What is the standard form of the equation 2(x−1)² + 3(x+2)² = 65?
Answer and explanation
Correct answer: 5x² + 8x − 51 = 0
Expanding the brackets gives 2x² − 4x + 2 + 3x² + 12x + 12 = 65. Combining like terms, 5x² + 8x + 14 = 65, and moving 65 to the left gives 5x² + 8x − 51 = 0. Therefore, option A is correct. Option B has an incorrect sign for the linear term. Exam tip: Expand each squared binomial carefully before rearranging the equation into ax² + bx + c = 0.
Frequently asked questions
What is the correct answer to this question?
5x² + 8x − 51 = 0
Why is this the correct answer?
Expanding the brackets gives 2x² − 4x + 2 + 3x² + 12x + 12 = 65. Combining like terms, 5x² + 8x + 14 = 65, and moving 65 to the left gives 5x² + 8x − 51 = 0. Therefore, option A is correct. Option B has an incorrect sign for the linear term. Exam tip: Expand each squared binomial carefully before rearranging the equation into ax² + 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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