Question

If the sum of the zeroes of the quadratic polynomial kx2 + 2x + 3k is equal to
their product, then find the value of k.​

Answer 1

Step-by-step explanation:

given polynomial = kx

2

−2x−3k

if ax

2

+bx+c is a polynomial then its sum of roots is given by

a

−b

and product of roots is given by

a

c

∴ sum of roots of given polynomial =

k

−(−2)

=

k

2

product of roots =

k

−3k

=−3

it is given that sum of roots = product of roots

k

2

=−3

k=

3

−2

Answer 2

$k {x}^{2} + 2x + 3k$

a = k

b = 2

c = 3k

sum of the zeros = -b/a = -2/k

product of the zeros = c/a = 3k/k = 3.

sum of zeros = product of the zeros

$\frac{ - 2}{k} = 3$

$k = - \frac{2}{3}$