If 3 and 5 are the roots of the equation \(ax^2+bx+15=0\), what is the value of \(a\)?
Answer and explanation
Correct answer: 1
For a quadratic equation \(Ax^2+Bx+C=0\), the product of its roots is \(\frac{C}{A}\). Here, the product is \(3\times5=15\), while \(\frac{C}{A}=\frac{15}{a}\). Thus, \(\frac{15}{a}=15\), giving \(a=1\). The value 15 is the constant term, not the coefficient \(a\). Exam tip: use \(\frac{c}{a}\) for the product of roots and \(-\frac{b}{a}\) for their sum.
Frequently asked questions
What is the correct answer to this question?
1
Why is this the correct answer?
For a quadratic equation \(Ax^2+Bx+C=0\), the product of its roots is \(\frac{C}{A}\). Here, the product is \(3\times5=15\), while \(\frac{C}{A}=\frac{15}{a}\). Thus, \(\frac{15}{a}=15\), giving \(a=1\). The value 15 is the constant term, not the coefficient \(a\). Exam tip: use \(\frac{c}{a}\) for the product of roots and \(-\frac{b}{a}\) for their sum.
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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