Question

Q2.If the sum of the zeroes of the polynomial p(x) = kx' +2x+3k is equal to their product, then
find two value of 'k'.​ .​

Answer 1

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-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

brainly.in/question/10399854

Answer 2

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Kx² + 2x + 3k

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

Finding sum of the zeroes ,

α + β = - b /a

α + β = - 2 / k

Now , Finding the product of the zeroes,

αβ = c / a

αβ = 3k / k = 3

Given that :-

Sum of the zeroes = Product of the zeroes

i.e , α + β = αβ

$\begin{gathered}\dag\;{\underline{\frak{Putting\:the\:values,}}}\\ \\\end{gathered}$

- 2 / k = 3

- 2 = 3k

↠ k = - 2 / 3

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