Question

Q. 8 The zeroes of the quadratic polynomial x2 + kx + k where k = 0,
(a) cannot both be positive
(b) cannot both be negative
(c) are always unequal
(d) are always equal
Plz give a detailed and simplified answer​

Answer 1

Since you didnt reposted question am explaining here

x2+kx+k,k≠0

roots or zeroes=(-k+√(k∧2-4k))/2,(-k-√(k∧2-4k))/2

since k≠0 ,roots can't be zero

the nature of root depends on √(k∧2-4k )

k<0 then √(k∧2-4k)>k so roots will be one  positive and one negative

if k>0 then √(k∧2-4k) < k both roots will be  negative

so both roots can't be positive

Answer 2

Answer:

The zeroes of this polynomial cannot be positive.

Let us try solving the quadratic by giving values to k.

If we take k as 5 and solve, we will get x as -1.38 and -3.61.

On the other hand, if we take k as 4, then we will get x as -2.

If k is taken to be negative such as -3, then the roots will be both positive and negative.

Hence option A.