If a and b are real numbers, a \(\neq\) b, and \(x^2-(a+b)x+ab=0\), what will be the nature of the roots of this quadratic equation?
Answer and explanation
Correct answer: Two distinct real roots
The equation can be factorised as \(x^2-(a+b)x+ab=(x-a)(x-b)=0\). Hence, its roots are \(x=a\) and \(x=b\). Since a and b are real and unequal, the roots are distinct and real. Equal roots would occur only when \(a=b\), and the roots need not be irrational. Exam tip: Use the discriminant \(D=(a-b)^2\); when \(a\neq b\), \(D>0\), which indicates two distinct real roots.
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What is the correct answer to this question?
Two distinct real roots
Why is this the correct answer?
The equation can be factorised as \(x^2-(a+b)x+ab=(x-a)(x-b)=0\). Hence, its roots are \(x=a\) and \(x=b\). Since a and b are real and unequal, the roots are distinct and real. Equal roots would occur only when \(a=b\), and the roots need not be irrational. Exam tip: Use the discriminant \(D=(a-b)^2\); when \(a\neq b\), \(D>0\), which indicates two distinct real roots.
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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