Which factorised form represents the equation \(x^2+7x+12=0\)?
Answer and explanation
Correct answer: \((x+3)(x+4)=0\)
To factorise the quadratic we look for two numbers whose product is 12 (the constant term) and whose sum is 7 (the coefficient of x). The pair 3 and 4 satisfy this, so \((x+3)(x+4)=0\) is the correct factorisation. By the zero-product property the roots are x = −3 and x = −4. Closest distractor (B) yields a sum of −7 (wrong sign), (C) yields sum 8, and (D) gives product −12 — hence they are incorrect. Exam tip: match pairs whose product equals c and whose sum equals b to factor quickly for integer-coefficient quadratics.
Frequently asked questions
What is the correct answer to this question?
\((x+3)(x+4)=0\)
Why is this the correct answer?
To factorise the quadratic we look for two numbers whose product is 12 (the constant term) and whose sum is 7 (the coefficient of x). The pair 3 and 4 satisfy this, so \((x+3)(x+4)=0\) is the correct factorisation. By the zero-product property the roots are x = −3 and x = −4. Closest distractor (B) yields a sum of −7 (wrong sign), (C) yields sum 8, and (D) gives product −12 — hence they are incorrect. Exam tip: match pairs whose product equals c and whose sum equals b to factor quickly for integer-coefficient quadratics.
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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