Question

The zeros of the quadratic polynomial x^2+ ax + b, a,b > 0 are
a) both positive
b) both negative
c) one positive one negative d) cannot say​

Answer 1

The zeros of the quadratic polynomial x^2+ ax + b:

1) A Quadratic polynomial is the polynomial of the variable and the constants with the highest degree of 2.

2) The zeroes of the quadratic equation are given by,

$\frac{-a+\sqrt{a^2-4ab} }{2}\\and\\\frac{-a-\sqrt{a^2-4ab} }{2}$

where clearly the zeroes depend upon the relation of the a and b so the nature of the zeroes cannot determine if we don't have any idea about the relation between the coefficients.

Hence the correct answer is (D) cannot say.

Answer 2

Answer:

B)Both positive

Step-by-step explanation:

We know that Alpha*beta=b

Alpha+beta=a

given that alpha and beta are positive

then there are 2 cases

1st case

both are positive

2nd case

both are negative and it is given that the sum of roots is positive

then we know that quadratic equation is of the form

x^2-(Alpha+beta)x+Alpha+beta

but it is given that 2nd term is positive it can be positive only if the sum of the roots are negative as -*-=+

Thus it should be both negative