What is the standard form of 8x − x² = 15 with a positive coefficient of x²?
Answer and explanation
Correct answer: x² − 8x + 15 = 0
A quadratic equation in standard form is ax² + bx + c = 0, and the question specifically requires the coefficient of x² to be positive. Start with 8x − x² = 15. Move 15 to the left: 8x − x² − 15 = 0, or equivalently −x² + 8x − 15 = 0. Since the x² coefficient is negative, multiply the entire equation by −1. This changes every sign and gives x² − 8x + 15 = 0. Therefore option A is correct. It is essential to change all terms, not just the x² term. Options B, C and D contain one or more incorrect signs and are not equivalent to the original equation.
Frequently asked questions
What is the correct answer to this question?
x² − 8x + 15 = 0
Why is this the correct answer?
A quadratic equation in standard form is ax² + bx + c = 0, and the question specifically requires the coefficient of x² to be positive. Start with 8x − x² = 15. Move 15 to the left: 8x − x² − 15 = 0, or equivalently −x² + 8x − 15 = 0. Since the x² coefficient is negative, multiply the entire equation by −1. This changes every sign and gives x² − 8x + 15 = 0. Therefore option A is correct. It is essential to change all terms, not just the x² term. Options B, C and D contain one or more incorrect signs and are not equivalent to the original equation.
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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