Question

if the sum of the zeros of the quadratic polynomial f x is equal to K X square + 2 X + 3 K is equal to their product find the value of k​

Answer 1

Answer:

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

Step-by-step explanation:

Given,

a quadratic equation,

$f(x) = k {x}^{2} + 2x + 3k$

Now,

we know that,

General form of a quadratic equation is

$f(x) = a {x}^{2} + bx + c$

Comparing the coefficients,

we get,

a = k

b = 2

c = 3k

Also,

we know that,

in a quadratic equation,

$\bold{Sum\:of\:roots = -\frac{b}{a}}$

$=>Sum\:of\:roots = -\frac{2}{k}$

And,

$\bold{Product\:of\:roots = \frac{c}{a}}$

$=>Product\:of\:roots = \frac{3k}{k}= 3$

But,

its being given that,

Sum of roots = Product of roots

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

Hence,

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