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If p(x)=x²+ax+b satisfies p(-2)=0 and p(5)=0, what is the value of a+b?
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Answer and explanation
Correct answer: -13
Since p(-2)=0 and p(5)=0, the zeros of the polynomial are -2 and 5. Therefore, p(x)=(x+2)(x-5)=x²-3x-10. Comparing coefficients gives a=-3 and b=-10, so a+b=-3+(-10)=-13. Remember that the sum of the zeros is 3, whereas a is its negative.
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What is the correct answer to this question?
-13
Why is this the correct answer?
Since p(-2)=0 and p(5)=0, the zeros of the polynomial are -2 and 5. Therefore, p(x)=(x+2)(x-5)=x²-3x-10. Comparing coefficients gives a=-3 and b=-10, so a+b=-3+(-10)=-13. Remember that the sum of the zeros is 3, whereas a is its negative.
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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