If the roots of the quadratic equation \(5x^2+px+q=0\) are \(3\) and \(-4\), what is the value of \(\frac{q}{5}\)?
Answer and explanation
Correct answer: \(-12\)
For a quadratic equation \(ax^2+bx+c=0\), the product of its roots is \(\frac{c}{a}\). Here, \(a=5\) and \(c=q\), so the product of the roots is \(\frac{q}{5}\). Therefore, \(\frac{q}{5}=3\times(-4)=-12\). The distractor \(12\) results from missing the negative sign. Exam tip: remember that the sum of roots is \(-\frac{b}{a}\), while their product is \(\frac{c}{a}\).
Frequently asked questions
What is the correct answer to this question?
\(-12\)
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, \(a=5\) and \(c=q\), so the product of the roots is \(\frac{q}{5}\). Therefore, \(\frac{q}{5}=3\times(-4)=-12\). The distractor \(12\) results from missing the negative sign. Exam tip: remember that the sum of roots is \(-\frac{b}{a}\), while their product is \(\frac{c}{a}\).
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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