Question

If the sum of the zeroes of the quadratic polynomial kx²+4x+3k is equal to their product,find the value of k

Answer 1

Answer:

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

ax²+bx+c , we get

a = k , b = 2 , c = 3k

\begin{gathered}i ) Sum \:of \:the \:zeroes = \frac{-b}{a}\\=\frac{-2}{k}--(1)\end{gathered}i)Sumofthezeroes=a−b=k−2−−(1)

\begin{gathered}ii) Product \:of \: the \: zeroes = \frac{c}{a}\\=\frac{3k}{k}\\=3--(2)\end{gathered}ii)Productofthezeroes=ac=k3k=3−−(2)

According to the problem given,

sum of the zeroes is equal to theirproduct.

\frac{-2}{k}=3k−2=3

\implies -2=3k⟹−2=3k

\implies \frac{-2}{3}=k⟹3−2=k

Therefore,

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

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