Question

if the some of the zeros of the polynomial p(x) =kx² + 2x+ 3k is equal to their product then find to value of k​

Answer 1

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Q) If the sum of the zeroes of the Polynomial p(x) = kx² + 2x + 3k is equal to the product of the zeroes then find the value of k .

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★ Given :

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

★ To Find :

• The value of K

★ Solution :

Standard Quadratic Equation is in the form :

$\boxed{ \sf \: a {x}^{2} + bx + c \: }$

So , here ,

• a = k
• b = 2
• c = 3k

Now , as we know that ,

$\mapsto \rm \: sum \: of \: zeroes = \frac{ - b}{a}$

$\leadsto \rm \: sum \: of \: zeroes = \frac{ - 2}{k} \: .....(i)$

and ,

$\mapsto \rm \: product \: of \: zeroes = \frac{c}{a} \:$

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

$\leadsto \rm \: product \: of \: zeroes = 3.....(ii)$

According to the Question ,

eq(i) = eq(ii)

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

$\longrightarrow \pink{\boxed{ \rm \: k = \frac{ - 2}{3} }}$

So , this is the required answer .