If \(x=-2\) is a root of \(x^2+px-6=0\), what is the value of \(p\)?
Answer and explanation
Correct answer: -1
Substitute the given root into the equation: \((-2)^2 + p(-2) - 6 = 0\) ⇒ \(4 - 2p - 6 = 0\) ⇒ \(-2 - 2p = 0\) ⇒ \(-2p = 2\) ⇒ \(p = -1\). A common mistake is to drop the negative sign on the \(px\) term, which would incorrectly give \(p=1\) (option A). Options C and D do not satisfy the equation when substituted. Exam tip: always substitute the root and simplify carefully, paying attention to signs.
Frequently asked questions
What is the correct answer to this question?
-1
Why is this the correct answer?
Substitute the given root into the equation: \((-2)^2 + p(-2) - 6 = 0\) ⇒ \(4 - 2p - 6 = 0\) ⇒ \(-2 - 2p = 0\) ⇒ \(-2p = 2\) ⇒ \(p = -1\). A common mistake is to drop the negative sign on the \(px\) term, which would incorrectly give \(p=1\) (option A). Options C and D do not satisfy the equation when substituted. Exam tip: always substitute the root and simplify carefully, paying attention to signs.
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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