If \(kx^2-14x+49=0\) has equal roots, what is the value of \(k\)?
Answer and explanation
Correct answer: 1
For equal roots, the discriminant must be zero: \(D=b^2-4ac=0\). Here, \(a=k\), \(b=-14\), and \(c=49\), so \(D=(-14)^2-4(k)(49)=196-196k\). Thus, \(196-196k=0\), giving \(k=1\). Exam tip: identify the coefficient of \(x^2\) as \(a=k\); the equation is quadratic only when \(k\neq 0\).
Frequently asked questions
What is the correct answer to this question?
1
Why is this the correct answer?
For equal roots, the discriminant must be zero: \(D=b^2-4ac=0\). Here, \(a=k\), \(b=-14\), and \(c=49\), so \(D=(-14)^2-4(k)(49)=196-196k\). Thus, \(196-196k=0\), giving \(k=1\). Exam tip: identify the coefficient of \(x^2\) as \(a=k\); the equation is quadratic only when \(k\neq 0\).
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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