If (x^2-14x+k=0) has equal roots, what is the value of (k)?
Answer and explanation
Correct answer: 49
A quadratic equation (ax^2+bx+c=0) has equal roots when its discriminant (D=b^2-4ac) is zero. Here, (a=1,b=-14,c=k), so (-14)^2-4(1)(k)=0, giving (196-4k=0) and hence (k=49). The value 196 results from forgetting to divide by 4. Exam tip: For equal roots, immediately use (D=0).
Frequently asked questions
What is the correct answer to this question?
49
Why is this the correct answer?
A quadratic equation (ax^2+bx+c=0) has equal roots when its discriminant (D=b^2-4ac) is zero. Here, (a=1,b=-14,c=k), so (-14)^2-4(1)(k)=0, giving (196-4k=0) and hence (k=49). The value 196 results from forgetting to divide by 4. Exam tip: For equal roots, immediately use (D=0).
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.
