If a = 0 and b = -2 in p(x) = x^3 + ax^2 + bx + 1, what will the polynomial be?
Answer and explanation
Correct answer: x^3 - 2x + 1
The governing concept is substitution of parameter values into a polynomial, followed by simplification. Start with p(x) = x^3 + ax^2 + bx + 1. Substituting a = 0 makes ax^2 = 0x^2 = 0, so the x^2 term disappears. Substituting b = -2 makes bx = -2x. Thus p(x) = x^3 + 0x^2 - 2x + 1, which simplifies to x^3 - 2x + 1. Therefore option A is correct. Option B uses the wrong sign for b, option C incorrectly places -2 on x^2, and option D omits the constant term and mishandles the substitution.
Frequently asked questions
What is the correct answer to this question?
x^3 - 2x + 1
Why is this the correct answer?
The governing concept is substitution of parameter values into a polynomial, followed by simplification. Start with p(x) = x^3 + ax^2 + bx + 1. Substituting a = 0 makes ax^2 = 0x^2 = 0, so the x^2 term disappears. Substituting b = -2 makes bx = -2x. Thus p(x) = x^3 + 0x^2 - 2x + 1, which simplifies to x^3 - 2x + 1. Therefore option A is correct. Option B uses the wrong sign for b, option C incorrectly places -2 on x^2, and option D omits the constant term and mishandles the substitution.
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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