Question

if sum of the zeros of kx² +3k+2x is equal to their product .find k

Answer 1

Answer:

Step-by-step explanation:kx²+3x+3k

Use ∆=0

b²-4ac=0

(3)²-4(k)(3k)=0

9-12k²=0

-12k²=-9

k²=9/12

k=+or-3/√12

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Answer 2

Answer:

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

Step-by-step explanation:

Given , the quadratic polynomial

kx² + 3k + 2x

= kx² + 2x + 3k

Here ,

a = k

b = 2

c = 3k

$let \: \: \alpha \: \: and \: \: \beta \: \: be \: the \: zeroes \: \\ of \: the \: polynomial$

Now ,

$sum \: of \: the \: zeroes = - \frac{ b}{a} \\ \\ \implies \alpha + \beta = - \frac{2}{k}$

And ,

$product \: of \: zeroes = \frac{ c}{a} \\ \\ \implies \alpha \beta = \frac{3k}{k} \\ \\ \implies \alpha \beta = 3$

Therefore , given that the sum of the zeroes is equal to the product of the zeroes, so :

$\alpha + \beta = \alpha \beta \\ \\ \implies - \frac{ 2}{k} = 3 \\ \\ \implies - 2 = 3k \\ \\ \implies \: k = - \frac{2}{3}$