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

Correct Question:

If the sum of the zeroes of the polynomial p(x) = kx²+2x+3k is equal to their product.

To Find:

The value of k

$\huge\bold{\gray{\sf{Answer:}}}$

$\bold{Explanation:}$

sum of zeroes is =>$\bold{\red{ - \frac{b}{a}}}$

✹$\bold{\red{ - \frac{b}{a}}}$= $\bold{\frac{-coefficient\:of\:x}{coefficient\: of\:x²} }$

Product of zeroes is =>$\bold{\blue{ \frac{c}{a}}}$

✹$\bold{\blue{ \frac{c}{a}}}$=$\bold{\frac{constant \:term}{coefficient\: of\:x²} }$

From above equation ,we get a=K ,b=2 and c=3k

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

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

In Question given that sum of zeroes is equal to the product of its zeroes,then

$\bold{\boxed{{\red{ - \frac{b}{a}}}=\bold{\blue{ \frac{c}{a}}}}}$

$= > - \frac{2}{k} = 3$

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

Answer 2

Answer:

given polynomial = kx2−2x−3k 

if ax2+bx+c is a polynomial then its sum of roots is given by a−b and product of roots is given by ac 

∴ sum of roots of given polynomial =k−(−2)=k2 

product of roots =k−3k=−3

 

it is given that sum of roots = product of roots 

k2=−3 

k=3−2