Question

If sum of zero of the quadratic polynomial f(x)kx*x +2*x+3*k is equal to their product. Find the value of k

Answer 1

Given: An equation kx² + 2x + 3k; the sum of its zeros = the product of its zeros.

To find: The value of k.

Answer:

We know that the geneal form of an equation is ax² + bx + c, where:

• The  sum of the zeros is given by -b/a.
• The product of the zeros is given by c/a.

From the given equation, we have:

• a = k
• b = 2
• c = 3k

Now, according to the question,

$\tt \dfrac{-b}{a}\ =\ \dfrac{c}{a}$

This implies that:

$\tt \dfrac{-2}{k}\ =\ \dfrac{3k}{k}\\\\\\-2\ =\ 3k\\\\\\\dfrac{-2}{3}\ =\ k$

Therefore, k = -2/3.

Answer 2

Answer:

$\implies$ k = -2/3

$\large\underline\mathrm{Given:-}$

• An equation kx² + 2x + 3k ; the Sum of it's zeroes = The products of it's zeroes.

$\large\underline\mathrm{To \: find}$

• The value of k.

$\large\underline\mathrm{Solution}$

$\implies$ The sum of the zero is given by -b/a.

$\implies$ The product of zero is given by c/a.

$\implies$ a = k

$\implies$ b = 2

$\implies$ c = 3k

Now,

$\implies$ -b/a = c/a

$\implies$ -2/k = 3k/k

$\implies$ -2 = 3k

$\implies$ k = -2/3

Thus,

k = -2/3