If the two roots of 8x^2+px+16=09 are equal, which values of 8p9 are possible?
Answer and explanation
Correct answer: 8p=89 or 8p=-89
For a quadratic equation 8ax^2+bx+c=09 to have equal roots, its discriminant 8D=b^2-4ac9 must be zero. Here, 8a=1,b=p,c=169, so 8D=p^2-4\times1\times16=p^2-64=09. Hence 8p^2=649 and 8p=\pm89, making option A correct. For the closest distractor, 8p=\pm49 gives a non-zero discriminant. Exam tip: whenever roots are equal, set the discriminant equal to zero first.
Frequently asked questions
What is the correct answer to this question?
8p=89 or 8p=-89
Why is this the correct answer?
For a quadratic equation 8ax^2+bx+c=09 to have equal roots, its discriminant 8D=b^2-4ac9 must be zero. Here, 8a=1,b=p,c=169, so 8D=p^2-4\times1\times16=p^2-64=09. Hence 8p^2=649 and 8p=\pm89, making option A correct. For the closest distractor, 8p=\pm49 gives a non-zero discriminant. Exam tip: whenever roots are equal, set the discriminant equal to zero first.
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.
