Question

If the sum of the zeros of the quadratic polynomial kx×x+2x+3k is equal to the product of its zeros , then find the value of 'k'​

Answer 1

Step-by-step explanation:

Sum of zeros of given polynomial = Product of its zeros

$= > \frac{ - b}{a} = \frac{c}{a}$

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

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

Answer 2

AnswEr

The value of k is -2/3

Given

The quadratic polynomial

kx² + 2x + 3k

The sum zeroes of the zeroes is equal to the product of its zeroes

To Find

The value of k

Solution

Let us consider the zeroes of the polynomial be α and β

Now we know that

sum of the zeroes = -coefficient of x/coefficient of x²

⇒α + β = -2/k

And again

Product of the zeroes =constant term/coefficient of x²

⇒αβ = 3k/k

⇒αβ = 3

Since

⇒α + β = αβ

⇒ -2/k = 3

⇒ -2 = 3k

⇒ k = -2/3