If the discriminant of a quadratic equation is \(D=(s-2)(s+5)\), where \(s\) is real, when will its roots be real and distinct?
Answer and explanation
Correct answer: \(s<-5\) or \(s>2\)
For a quadratic equation to have real and distinct roots, its discriminant must satisfy \(D>0\). Thus, \((s-2)(s+5)>0\). The zero points are \(s=2\) and \(s=-5\); the product is positive outside these points, giving \(s<-5\) or \(s>2\). In option B, \(D<0\), so the roots are non-real, while in option C, \(D=0\), so the roots are equal. Exam tip: for a product inequality, mark the zero points on a number line and check the sign in each interval.
Frequently asked questions
What is the correct answer to this question?
\(s<-5\) or \(s>2\)
Why is this the correct answer?
For a quadratic equation to have real and distinct roots, its discriminant must satisfy \(D>0\). Thus, \((s-2)(s+5)>0\). The zero points are \(s=2\) and \(s=-5\); the product is positive outside these points, giving \(s<-5\) or \(s>2\). In option B, \(D<0\), so the roots are non-real, while in option C, \(D=0\), so the roots are equal. Exam tip: for a product inequality, mark the zero points on a number line and check the sign in each interval.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Nature of Roots.
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