A situation involving a rectangle leads to the quadratic equation \(t^2-8t+16=0\). What is the nature of its roots?
Answer and explanation
Correct answer: Two equal real roots (\(D=0\))
Here, \(a=1\), \(b=-8\), and \(c=16\). Thus, the discriminant is \(D=b^2-4ac=(-8)^2-4(1)(16)=64-64=0\). When \(D=0\), a quadratic equation has two equal real roots. In fact, \(t^2-8t+16=(t-4)^2\), so both roots are \(t=4\). Option B applies only when \(D>0\), which gives distinct real roots. Exam tip: To determine the nature of roots, first check the sign of the discriminant.
Frequently asked questions
What is the correct answer to this question?
Two equal real roots (\(D=0\))
Why is this the correct answer?
Here, \(a=1\), \(b=-8\), and \(c=16\). Thus, the discriminant is \(D=b^2-4ac=(-8)^2-4(1)(16)=64-64=0\). When \(D=0\), a quadratic equation has two equal real roots. In fact, \(t^2-8t+16=(t-4)^2\), so both roots are \(t=4\). Option B applies only when \(D>0\), which gives distinct real roots. Exam tip: To determine the nature of roots, first check the sign of the discriminant.
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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