If the zeroes of (x^2+px+16) are equal and negative, what is (p)?
Answer and explanation
Correct answer: 8
Use the relation between the zeroes and coefficients of a quadratic. If the equal zeroes are r and r, their product is r^2 = 16, so r = 4 or r = -4. Since the question says the zeroes are negative, r = -4. Their sum is therefore -8. For x^2+px+16, the sum of zeroes equals -p, so -p = -8 and p = 8. Hence option A is correct. Option B results from confusing p with the sum of the zeroes. Options C and D do not satisfy both the product condition and the required negative repeated roots. Equivalently, the discriminant p^2-64 must be zero, giving p = ±8, and negativity selects p = 8.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
Use the relation between the zeroes and coefficients of a quadratic. If the equal zeroes are r and r, their product is r^2 = 16, so r = 4 or r = -4. Since the question says the zeroes are negative, r = -4. Their sum is therefore -8. For x^2+px+16, the sum of zeroes equals -p, so -p = -8 and p = 8. Hence option A is correct. Option B results from confusing p with the sum of the zeroes. Options C and D do not satisfy both the product condition and the required negative repeated roots. Equivalently, the discriminant p^2-64 must be zero, giving p = ±8, and negativity selects p = 8.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Polynomials in one variable.
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