Question

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

Answer 1

Answer:

$value \: of \: k = \frac{-2}{3}$

Step-by-step explanation:

Compare given Quadratic polynomial kx²+2x+3k by

ax²+bx+c , we get

a = k , b = 2 , c = 3k

$i ) Sum \:of \:the \:zeroes = \frac{-b}{a}\\=\frac{-2}{k}--(1)$

$ii) Product \:of \: the \: zeroes = \frac{c}{a}\\=\frac{3k}{k}\\=3--(2)$

According to the problem given,

sum of the zeroes is equal to their product.

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

$\implies -2=3k$

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

Therefore,

$value \: of \: k = \frac{-2}{3}$

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Answer 2

-2/3 is the value of k

Step-by-step explanation:

In case of a polynomial kx²+2x+3k, then its sum of roots is given by -b/a while the product of zeroes is found by c/a

a = k

b = 2

c = 3k

∵ Sum of the zeroes = -b/a

= -2/k - (-1)

and the product of zeroes = c/a

= 3k/k

= 3 - (-2)

As per the question,

The sum of the zeroes is equal to their product, so

-2/k = 3

-2 = 3k

-2/3 = k

Therefore, k = -2/3

Learn more: the sum of the zeroes of the quadratic polynomial

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