Question

If alpha beta are the zeros of the polynomial x square - 2 X + 3 k such that alpha + beta is equal to Alpha Beta then K = ?​

Answer 1

Step-by-step explanation:

given,

alpha and beta are the zeroes of the polynomial x²-2x+3k

alpha+beta=alpha×beta

WE KNOW

alpha + beta = -b/a

alpha × beta = c/a

alpha + beta= -(-2)/1=2

alpha × beta = 3k/1=3k

ATQ

alpha+beta=alpha×beta

2=3k

k=2/3

Answer 2

The value of k is equal to $\dfrac{2}{3}.$

Step-by-step explanation:

Given,

α, β are the zeros of the polynomial $x^2-2x+3k$

To find, the value of k = ?

∵ α + β = αβ       .......(1)

We know that,

The sum of the roots,

$\alpha+\beta=-\frac{b}{a}$

$=-\frac{-2}{1}=2$

Also,

The product of the roots,

$\alpha\beta=\frac{c}{a}$

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

Now, equation (1) becomes

$2=3k$

⇒$k=\dfrac{2}{3}$

Hence, the value of k is equal to $\dfrac{2}{3}.$