If ((k-2)x^2+4x+1=0) has equal roots, what is the value of (k)?
Answer and explanation
Correct answer: 6
For a quadratic equation (ax^2+bx+c=0) to have equal roots, its discriminant (D=b^2-4ac) must be zero. Here, a=k-2, b=4, c=1, so D=16-4(k-2)=0, giving k=6. Note that when k=2, the equation becomes linear rather than quadratic, so it cannot represent equal roots of a quadratic equation. Exam tip: Set the discriminant equal to zero whenever a quadratic is stated to have equal roots.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
For a quadratic equation (ax^2+bx+c=0) to have equal roots, its discriminant (D=b^2-4ac) must be zero. Here, a=k-2, b=4, c=1, so D=16-4(k-2)=0, giving k=6. Note that when k=2, the equation becomes linear rather than quadratic, so it cannot represent equal roots of a quadratic equation. Exam tip: Set the discriminant equal to zero whenever a quadratic is stated to have equal roots.
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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