For which values of \\(k\\) will the equation \\(x^2-2(k-3)x+16=0\\) have equal roots?
Answer and explanation
Correct answer: \\(k=7\\) or \\(k=-1\\)
A quadratic equation \\(ax^2+bx+c=0\\) has equal roots when its discriminant satisfies \\(D=b^2-4ac=0\\). Here, \\(a=1\\), \\(b=-2(k-3)\\), and \\(c=16\\). Therefore, \\(4(k-3)^2-64=0\\), so \\(k-3=\\pm4\\), giving \\(k=7\\) or \\(k=-1\\). Exam tip: For equal-root questions, begin by setting the discriminant equal to zero.
Frequently asked questions
What is the correct answer to this question?
\\(k=7\\) or \\(k=-1\\)
Why is this the correct answer?
A quadratic equation \\(ax^2+bx+c=0\\) has equal roots when its discriminant satisfies \\(D=b^2-4ac=0\\). Here, \\(a=1\\), \\(b=-2(k-3)\\), and \\(c=16\\). Therefore, \\(4(k-3)^2-64=0\\), so \\(k-3=\\pm4\\), giving \\(k=7\\) or \\(k=-1\\). Exam tip: For equal-root questions, begin by setting the discriminant equal to zero.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Nature of Roots.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
