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

Answer:

$\huge{\underline{\underline{\tt{\greenſ.Question}}}}$

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'. !

$\huge{\underline{\underline{\tt{\greenſ.To\ find : Value\ of\ K }}}}$

$\huge{\underline{\underline{\tt{\blueſ.Answer}}}}$

$given\ polynomial = kx²+2x+3k$

if ax²+bx+c is a polynomial then its sum of roots is given by -b/a and the product of root is given by c/a

.•. Sum of roots of Given polynomial= -(2)/k =-2/k

and product of roots =3k/k =3

$It\ is\ Given\ that,$

Sum of roots = product of roots

-2/K=3

$\huge{\underline{\underline{\tt{\blueſ.K=-2/3}}}}$

---------------------

$\huge{\underline{\underline{\tt{\pinkſ.Second\ way\ to\ solve}}}}$

$\huge{\underline{\underline{\tt{\redſ.Given\ that }}}}$ :

Polynomial, p(x) = kx²+2x+3k.

Sum of zeroes = Product of zeroes.

$\huge{\underline{\underline{\tt{\blueſ.To\ Find }}}}$

• The value of k.

$\huge{\underline{\underline{\tt{\pinkſ.Solution}}}}$

Given, polynomial, p(x) = kx²+2x+3k.

$On comparing with, ax? + bx + c,$

$\huge{\underline{\underline{\tt{\greenſ.We\ get;}}}}$

→ a=k, b = 2, c = 3k

$Sum\ of\ zeroes,$

→ α+ b = -b/a

= -2/k

Product of zeroes,

αß = c/a

αß = 3k/k

aß = 3

Given, sum of zeroes = product of zeroes. =

- -2/k = 3

= -2 = 3k

- k = -2/3

$\huge{\underline{\underline{\tt{\redſ. Hence, k =-2/3.}}}}$

Answer 2

$\bf \large{ \underline{ \underline{ \orange{Correct \: question : }}}}$

$\bf \small{If \: the \: sum \:o f \: the \: zeroes \: of \: polynomial} \\ \bf \small{p(x) = k {x}^{2} + 2x + 3k \: is \: equal \: to \: their} \\ \bf \small {product \: then \: find \: the \: value \: of \: k}$

$\bf \large { \underline{ \underline{ \pink{Given : }}}}$

$\bf \small{sum \: of \: zeroes \: and \: product \: of \: zeroes \: of \: } \\ \bf \small{ \: polynomial \: k {x}^{2} + 2x + 3k \: is \: equal}$

$\bf \large{ \underline{ \underline{ \green{Required \: answer : }}}}$

$\bf \small{Value \: of \: k}$

$\bf \large{ \underline{ \underline { \blue{Solution : }}}}$

$\bf \small{in \: polynomial \: k {x}^{2} + 2x + 3k} \\ \bf \small{a =k , \: b = 2 \: and \: c = 3k}$

$\small \therefore \bf \small {sum \: of \: zeroes\: = \frac { - b} {a} } \\ \sf \small{ = \frac{ - 2}{k}}$

$\sf \small{and \: sum \: of \: zeroes = \frac{c}{a} = \frac{3k}{k} = 3}$

$\bf \small{According \: to \: question} \\ \bf \small{sum \: of \: zeroes = product \: of \: zeroes}$

$\sf \small\therefore{ \frac{ - 2}{k} = 3}$

$\sf \small\implies{3k = - 2}$

$\sf \small \implies{k = \frac{ - 2}{3} }$

$\bf\small\therefore{k = \frac{-2}{3}$