Which option shows the mistake while converting (x^2=6x+7) to standard form?
Answer and explanation
Correct answer: (x^2+6x+7=0)
The standard form of a quadratic equation is usually written as ax^2 + bx + c = 0. Starting with x^2 = 6x + 7, move every term on the right to the left side. When a term crosses the equality sign, its sign changes: 6x becomes -6x and 7 becomes -7. Therefore, the correct standard form is x^2 - 6x - 7 = 0.
Option A is this correct form. Option B writes x^2 + 6x + 7 = 0, which changes neither sign and is not equivalent to the original equation. Option C, x^2 - 6x = 7, is an equivalent rearrangement, but it is not yet the usual standard form because the constant has not been moved to the left. Option D simply repeats the original equation. Hence option B shows the error.
Frequently asked questions
What is the correct answer to this question?
(x^2+6x+7=0)
Why is this the correct answer?
The standard form of a quadratic equation is usually written as ax^2 + bx + c = 0. Starting with x^2 = 6x + 7, move every term on the right to the left side. When a term crosses the equality sign, its sign changes: 6x becomes -6x and 7 becomes -7. Therefore, the correct standard form is x^2 - 6x - 7 = 0.
Option A is this correct form. Option B writes x^2 + 6x + 7 = 0, which changes neither sign and is not equivalent to the original equation. Option C, x^2 - 6x = 7, is an equivalent rearrangement, but it is not yet the usual standard form because the constant has not been moved to the left. Option D simply repeats the original equation. Hence option B shows the error.
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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