Question

find the roots of the 3x2-5x+2=0
​

Answer 1

Answer:

1 and 2/3

Step-by-step explanation:

Given: - 3x2-5x+2=0

on comparing this equation with ax2+bx+c=0,  

we get; a=3, b=-5 and c=2

Now,

    D (Discriminant) = b2−4ac

                              = (-5)2−4×3×2

                              =25-24

                              =1

        x= -b±√D/2a

          = -(-5) ±√1/2*3

          = 5 ± 1/6

Then,

       x=5+1/6  =6/6  =1                          

&

x=5-1/6 = 4/6 = 2/3

Answer 2

$\large\bold\red{Question}$

find the roots of the 3x2-5x+2=0

$\large\bold\blue{\underline{\underline{Solution}}}$

$\sf{Step\:1:}$ Calculate the product

$\implies \sf \red3x \red{ \times 2} - 5x + 2 = 0$

$\implies \sf 6x - 5x + 2 = 0$

$\sf{Step\:2:}$ Collect like terms by subtracting their coefficients

$\implies \sf \red{6x - 5x} + 2 = 0$

$\implies \sf(6 - 5)x$

Then, Subtract the numbers

$\implies \sf1x$

$\sf\red{Note:}$ When the term has a coefficient of 1, it doesn't have to be written.

$\implies \sf \: x$

$\large\bold\red{WHY?}$

$\bold\red{Why\:the\:coefficient\:1\:doesn't\:have\:to\:be\:written?}$

Because the coefficient 1 doesn't have to be written because it's doesn't affect the value of the term.

$\sf{Lastly:}$ Move constant to the right by adding it's opposite to both sides

$\implies \sf \: x + 2 = 0$

$\implies \sf \: x + 2 \red{ - 2} = 0 \red{ - 2}$

$\large\bold\red{WHY?}$

$\bold\red{Why\:move\:a\:constant\:to\:the\:right?}$

I want to move the constant to the right because mathematicians agreed upon a convention that constants in equations and inequalities always need to be on the right-hand side.

Then, the opposite term needs to be added to both sides to preserve the relation between the sides, according to the addition and subtraction property of equality/inequality.

$\bold\red{Note:}$ Since the opposite add up to zero, remove them from the expression

$\implies \sf \: x \red{ + 2 - 2} = 0 - 2$

$\implies \sf \: x = 0 - 2$

$\large\bold\red{WHY?}$

$\bold\red{Why\:do\:two\:opposite\:add\:up\:to\:zero?}$

Because the Inverse Property of Addition states that two opposite numbers add up to zero 0.

Since adding or subtarcting 0 doesn't change the value of the expression, we can just remove it.

$\bold\red{Note:}$ When adding or subtarcting 0, the quantity does not change

$\implies \sf \: x + 2 - 2 = \red0 - 2$

$\implies \sf \: x = - 2$

$\sf \: thus \: the \: root \: is \: \green{ \boxed { \boxed {\sf{ - 2}}}}$

hope this help!