What are the roots of the equation \(7x^2-19x-6=0\)?
Answer and explanation
Correct answer: \(x=3,\,-\frac{2}{7}\)
The quadratic factors as \(7x^2-19x-6=(7x+2)(x-3)\). Therefore, \((7x+2)(x-3)=0\) gives \(x=-\frac{2}{7}\) or \(x=3\). In option B, the signs of both roots are incorrect. Exam tip: After factorisation, set each factor equal to zero and carefully reverse the sign when isolating the root.
Frequently asked questions
What is the correct answer to this question?
\(x=3,\,-\frac{2}{7}\)
Why is this the correct answer?
The quadratic factors as \(7x^2-19x-6=(7x+2)(x-3)\). Therefore, \((7x+2)(x-3)=0\) gives \(x=-\frac{2}{7}\) or \(x=3\). In option B, the signs of both roots are incorrect. Exam tip: After factorisation, set each factor equal to zero and carefully reverse the sign when isolating the root.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Methods of Solving Quadratic Equations.
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