Question

yadi bahupad p[x]= kx2 +2x+3k ke zero's ka yog unke gudanfal ke barabar hoto 'k' ka man gyat kro?

Answer 1

☯︎ Qᴜᴇsᴛɪᴏɴ

if the sum of the zeroes of the polynomial p(x) = kx²+2x+3k is equal to their products, then find two value of ‘k’.

☯︎ Aɴsᴡᴇʀ

we have a quadratic polynomial,

• kx² + 2x + 3k = 0

and

• sum of zeroes = product of zeroes

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firstly compare the quadratic polynomial with ax² + bc + c

here, kx² + 2x + 3k

• a = k
• b = 2
• c = 3k

we know that,

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

and

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

and here,

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

then,

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

and

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

__________________________

and it is given that,

• sum of zeroes = product of zeroes

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

so, value of k is 3/-2