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The value of a and b, if the zeros of x^2+(a+5)x-(b-4) are -5 and 9 will be _________(a) 47, -5(b) -5, 47(c) -9, 49(d) -4, 45This question was posed to me during an interview.The origin of the question is Zeros and Coefficients of Polynomial topic in portion Polynomials of Mathematics – Class 10

Answer» RIGHT choice is (C) -9, 49

Explanation: The ZEROS of the POLYNOMIAL are -5 and 9.

Hence, α=-5, β=9

The polynomial is x^2+(a+5)x-(b-4).

Sum of zeros or α+β=-5+9 = \(\FRAC {-coefficient \, of \, x}{coefficient \, of \, x^2} = \frac {a+5}{1}\)

-4=a+5

a = -9

Product of zeros or αβ = -45 = \(\frac {constant \, term}{coefficient \, of \, x^2} = \frac {-(b-4)}{1}\)

-45=-b+4

b=49


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