If p(x)=x²+ax+b, p(1)=0, and p(2)=0, what is a+b?
Answer and explanation
Correct answer: −1
Use the given zero conditions by substituting the corresponding values into the polynomial. From p(1)=0, we get 1+a+b=0, so a+b=−1 immediately. For verification, p(2)=0 gives 4+2a+b=0. Subtracting the first equation from the second gives 3+a=0, hence a=−3; substituting back gives b=2. Therefore a+b=−3+2=−1, confirming option A. The roots are 1 and 2, so the polynomial can also be written as (x−1)(x−2)=x²−3x+2. Option C, which was previously marked, is incorrect; the conditions clearly force the sum of the coefficients a and b to be −1.
Frequently asked questions
What is the correct answer to this question?
−1
Why is this the correct answer?
Use the given zero conditions by substituting the corresponding values into the polynomial. From p(1)=0, we get 1+a+b=0, so a+b=−1 immediately. For verification, p(2)=0 gives 4+2a+b=0. Subtracting the first equation from the second gives 3+a=0, hence a=−3; substituting back gives b=2. Therefore a+b=−3+2=−1, confirming option A. The roots are 1 and 2, so the polynomial can also be written as (x−1)(x−2)=x²−3x+2. Option C, which was previously marked, is incorrect; the conditions clearly force the sum of the coefficients a and b to be −1.
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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