If 2 is subtracted from each root of the equation \(x^2-6x-16=0\), what is the product of the resulting roots?
Answer and explanation
Correct answer: -24
The roots of the equation are 8 and -2, since \(x^2-6x-16=(x-8)(x+2)\). After subtracting 2 from each root, the new roots are 6 and -4, whose product is \(6\times(-4)=-24\). Remember that the transformation must be applied to both roots; changing only one root gives an incorrect result.
Frequently asked questions
What is the correct answer to this question?
-24
Why is this the correct answer?
The roots of the equation are 8 and -2, since \(x^2-6x-16=(x-8)(x+2)\). After subtracting 2 from each root, the new roots are 6 and -4, whose product is \(6\times(-4)=-24\). Remember that the transformation must be applied to both roots; changing only one root gives an incorrect result.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.
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