Question : The zeroes of the quadratic polynomial x²+99x+127, are
a) both positive
b) both negative
c) one positive and one negative
d) both equal.
Doubt by Sachin
Solution : Solution :
x²+99x+127
Here
a=+1
a=+1
b=+99
c=+127
We know,
Product of zeroes = c/a
Product of zeroes = c/a
αβ = c/a
αβ = 127/1
αβ = 127
Here product of zeroes is coming positive which indicates that both the zeroes of the polynomials have the same signs i.e. either α & β both are +ve or both are -ve.
Also
Sum of zeroes = -b/a
α+β = -b/a
α+β = -99/1
α+β = -99
Here sum of zeroes is coming negative, hence both the zeroes of the polynomial are not positive because if both of them are positive then their sum can't be -ve. It simply indicated that both the zeros of the polynomial are -ve.
Hence, b) both negative, is the correct option.