If the product of the zeroes of the polynomial \(p(x)=3x^2-10x+m\) is \(\frac{4}{3}\), what is the value of \(m\)?
Answer and explanation
Correct answer: 4
For a quadratic polynomial \(ax^2+bx+c\), the product of its zeroes is \(\frac{c}{a}\). Here, \(a=3\) and \(c=m\), so the product is \(\frac{m}{3}\). Therefore, \(\frac{m}{3}=\frac{4}{3}\), which gives \(m=4\). Exam tip: remember that the sum of zeroes is \(-\frac{b}{a}\), while their product is \(\frac{c}{a}\).
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
For a quadratic polynomial \(ax^2+bx+c\), the product of its zeroes is \(\frac{c}{a}\). Here, \(a=3\) and \(c=m\), so the product is \(\frac{m}{3}\). Therefore, \(\frac{m}{3}=\frac{4}{3}\), which gives \(m=4\). Exam tip: remember that the sum of zeroes 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: Polynomials. Topic: Polynomials in one variable.
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