Question

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, 45

This 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 1

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