Question

alpha and bita are roots of polynomial p (x)=x ²-3x+2m such that alpha × bita =alpha + bita then m=???​

Answer 1

Answer:

3/2

Step-by-step explanation:

In the polynomials of form x² - Sx + P, S is the sum and P is the product  of roots.  If α and β are the roots.

S = α + β = 3   ;   P = αβ = 2m

 In question,

⇒ αβ = α + β

⇒ 2m = 3

⇒ m = 3/2

∴ value of m is 3/2

Answer 2

Answer:

Required value of m is 1.5.

Step-by-step explanation:

Given polynomial,

$p(x) = {x}^{2} - 3x + 2m$

Let,

$p(x) = 0$

${x}^{2} - 3x + 2m = 0.....(1)$

We know if

$a {x}^{2} + bx + c = 0$ is a equation then sum of roots of the equation is $- \frac{b}{a}$

and product of roots of the equation is $\frac{c}{a}$

We are comparing equation (1) with $a {x}^{2} + bx + c = 0$

and get,

$a = 1 \\ b = - 3 \\ c = 2m$

Given that $\alpha \: and \: \beta$ are roots of equation (1),

So,

$\alpha + \beta = - (\frac{ - 3}{1}) = 3 \\ \alpha \beta = \frac{2m}{1} = 2m$

Again given that,

$\alpha \beta = \alpha + \beta \\ 2m = 3 \\ m = \frac{3}{2} \\ m = 1.5$

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