What is the standard form of \((x-2)(x+3)+(2x-1)(x-4)=0\)?
Answer and explanation
Correct answer: \(3x^2-8x-2=0\)
Expanding the two products gives \((x-2)(x+3)=x^2+x-6\) and \((2x-1)(x-4)=2x^2-9x+4\). Combining like terms, \(x^2+2x^2=3x^2\), \(x-9x=-8x\), and \(-6+4=-2\). Hence the standard form is \(3x^2-8x-2=0\). Option B has the wrong sign for the linear term. Exam tip: expand each bracket carefully, then combine the quadratic, linear, and constant terms separately.
Frequently asked questions
What is the correct answer to this question?
\(3x^2-8x-2=0\)
Why is this the correct answer?
Expanding the two products gives \((x-2)(x+3)=x^2+x-6\) and \((2x-1)(x-4)=2x^2-9x+4\). Combining like terms, \(x^2+2x^2=3x^2\), \(x-9x=-8x\), and \(-6+4=-2\). Hence the standard form is \(3x^2-8x-2=0\). Option B has the wrong sign for the linear term. Exam tip: expand each bracket carefully, then combine the quadratic, linear, and constant terms separately.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Introduction to Quadratic Equations.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
