If p(x) = x^4 + mx^2 + 16 can be written as (x^2 - 4)^2, what is m?
Answer and explanation
Correct answer: -8
The governing concept is the algebraic identity (a - b)^2 = a^2 - 2ab + b^2. Here, take a = x^2 and b = 4. Therefore, (x^2 - 4)^2 = (x^2)^2 - 2(x^2)(4) + 4^2 = x^4 - 8x^2 + 16. Comparing this expression with p(x) = x^4 + mx^2 + 16, the coefficient of x^2 must be the same in both forms. Hence m = -8, so option A is correct. The values -4 and 4 do not give the required middle term, while 8 has the wrong sign.
Frequently asked questions
What is the correct answer to this question?
-8
Why is this the correct answer?
The governing concept is the algebraic identity (a - b)^2 = a^2 - 2ab + b^2. Here, take a = x^2 and b = 4. Therefore, (x^2 - 4)^2 = (x^2)^2 - 2(x^2)(4) + 4^2 = x^4 - 8x^2 + 16. Comparing this expression with p(x) = x^4 + mx^2 + 16, the coefficient of x^2 must be the same in both forms. Hence m = -8, so option A is correct. The values -4 and 4 do not give the required middle term, while 8 has the wrong sign.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Polynomials in one variable.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
