If the equation \(kx^2-8x+16=0\) has equal roots and \(k\ne0\), what is the value of \(k\)?
Answer and explanation
Correct answer: 1
For equal roots of a quadratic equation \(ax^2+bx+c=0\), the discriminant must be zero: \(D=b^2-4ac=0\). Here, \(a=k\), \(b=-8\), and \(c=16\), so \(D=(-8)^2-4(k)(16)=64-64k\). Thus, \(64-64k=0\), giving \(k=1\). Exam tip: Whenever equal roots are mentioned, immediately use the condition \(D=0\).
Frequently asked questions
What is the correct answer to this question?
1
Why is this the correct answer?
For equal roots of a quadratic equation \(ax^2+bx+c=0\), the discriminant must be zero: \(D=b^2-4ac=0\). Here, \(a=k\), \(b=-8\), and \(c=16\), so \(D=(-8)^2-4(k)(16)=64-64k\). Thus, \(64-64k=0\), giving \(k=1\). Exam tip: Whenever equal roots are mentioned, immediately use the condition \(D=0\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.
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