Question

If alpha and beta are the roots of the equation 3x square-5x+2=0, then find the value of alpha - beta​

Answer 1

Step-by-step explanation:

roots of equation are ÷

3x^2 -5x - 2 =0

3x^2 -6x + 1x - 2 =0

3x (x -2) +1 (x -2) =0

(3x+1)(x-2) =0

-1/3 & +2 are zeros

now

alpha - beta = -1/3 - 2

(-1 - 6)/3

-7/6

or

2 -(-1/3)

2 + 1/3

7/6

Answer 2

Given:

α and  β  are roots of the given equation 3x² - 5x +2=0

To find:

The value of α - β 

Solution:

we have

3x² -5x +2=0

Now, by splitting the middle term

we get,

=> 3x²-5x+2=0

=> 3x² -3x -2x +2=0

=> 3x(x-1)-2(x-1)=0

=> (x-1)(3x-2)=0

=> x=1 , x= 2/3

Hence, 1 and 2/3 are zeroes(roots) of the given equation.

So,

α = 1,  β = 2/3

Now,

substituting values in α - β 

we get,

$1 - \frac{2}{3 \: } \: = \frac{3 - 2}{3}$ = 1/3

=>  α - β =1/3