Question

The zeroes of the quadratic polynomial x2 +kx+k ,k not equal to 0 cannot both be positive. Explain the statement.How can you prove it?

Answer 1

K is not equal to zero

Answer 2

The zeroes of the quadratic polynomial $x^{2}+kx+k,$ k≠0 cannot both be positive.

Proof:

        Given equation is

                $x^{2}+kx+k$, k≠0

        Here,

                a = 1, b = c = k   ----------(1)

         Case (i): k < 0

                a > 0, b < 0, c < 0   [from (1)]

           ⇒ Both zeroes have opposite signs   -------------(2)

        Case (ii): k > 0

                a > 0, b > 0, c > 0    [from (1)]

           ⇒ Both zeroes are negative                --------------(3)

   ∴ From (1) and (2), we can conclude that both zeroes of given quadratic polynomial cannot be positive.