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:

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

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'. !

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

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

$given\ polynomial = kx²+2x+3k$

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

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

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

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

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

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

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