The zeroes of the quadratic polynomial x2+4x+3 . . .

Question : The zeroes of the quadratic polynomial x²+4x+3, are

a) both positive

b) both negative

c) one positive and one negative

d) both equal. 

Doubt by Mouli

Solution : 

x²+4x+3

Here 
a=+1

b=+4

c=+3

We know, 
Product of zeroes = c/a

αβ = c/a

αβ = 3/1

αβ = 3

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 = -4/1

α+β = -4

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. 

Similar 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.