Question

2.2. If the sum of the zeroes of the polynomial p(x) = kx²+2x+3k is equal to their product, then
find two value of 'k'.
यदि बहुपद p(x) = kx +2x+3k के शून्यांको का योग उनके गुणनफल के बराबर हो तो 'k' का
मान ज्ञात कीजिए।
16 represent Co-incident​

Answer 1

Answer:

I hope my answer will help you.

Answer 2

☯︎ Aɴsᴡᴇʀ

we have a quadratic equation

• p(x) = kx² + 2x + 3k
• sum of zeroes = product of zeroes

firstly compare the quadratic polynomial with p(x) = ax² + bx + c

so, here kx² + 2x + 3k

• a = k
• b = 2
• c = 3k

we know that

$\boxed{ \boxed{ \bold{sum \: of \: zeroes = \frac{ - coefficient \: of \: x}{coefficient \: of \: {x}^{2} } }}}$

and

$\boxed{ \boxed{ \bold{product \: of \: zeroes = \frac{constant \: ter}{coefficient \: of \: {x}^{2} } }}}$

and here, kx² + 2x + 3k

• coefficient of x² = k
• coefficient of x = 2
• constant term = 3k

then,

$\bold{sum \: of \: zeroes = \frac{ - 2}{k} }$

and

$\bold{product \: of \: zeroes = \frac{3 \cancel{k}}{ \cancel{k}} = 3 }$

and here it is given that,

• sum of zeroes = product of zeroes

$\bold{: \implies \frac{ - 2}{k} = 3} \: \: \\ \\ \bold{ : \implies \: - 2 = 3k } \\ \\ \bold{ : \implies \: \boxed{ \bold{k = \frac{ - 2}{ \: 3} }} }$

so, value of k is -2/3