Question

if sum of zeros of a quadratic polynomial k y square + 2 Y - 3 k is equal to twice the product find the value of k

Answer 1

sum of zeros of a quadratic polynomial = -b/a
product of zeros = c/a
a = k
b = 2
c = -3k
Let the product be x.
sum = 2x
=
$- \frac{b}{a} \\ = \frac{ - 2}{ - k} \\ = \frac{2}{k}$

product
$= \frac{ - 3k}{k }$
sum = 2 x product
$\frac{2}{k} = 2 \times \frac{ - 3k}{k} \\ = \frac{2}{k} = - 6 \\ - 6k = 2 \\ k = \frac{2}{ - 6} \\ k = \frac{ - 1}{3}$

Answer 2

here you go ☆☆


given,


sum of p(x) = 2× product of p(x)


$sum = \frac{ - b}{a} = \frac{ - 2}{k}$


$product = \frac{ - 3k}{k}$



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


$\frac{ - 2}{k} = - 6$

-6k = -2

$\boxed{k = \frac{1}{3} }$


hope it helps you........