Factorise the expression 6x^2-13x+6 and hence solve the equation 6x^2-13x+6=0

Part A

The factored form of the expression, 6·x² - 13·x + 6 is (2·x - 3) × (3·x - 2)

Part B

The solution of the equation 6·x² - 13·x + 6 = 0 are x = 3/2 or x = 2/3

Step-by-step explanation:

Part A

The given expression to factorize is 6·x² - 13·x + 6, which can be written as follows;

6·x² - 13·x + 6 = 6·x² - 4·x - 9·x + 6

The 13·x is split at - 4·x - 9·x

6·x² - 4·x - 9·x + 6

2·x·(3·x -2) - 3·(3·x - 2)

Bringing out the common factor (3·x - 2) gives;

(2·x - 3) × (3·x - 2)

Therefore, the expression 6·x² - 13·x + 6 in factored form is (2·x - 3) × (3·x - 2)

Part B

Solving the equation, 6·x² - 13·x + 6 = 0, therefore gives;

6·x² - 13·x + 6 = (2·x - 3) × (3·x - 2) = 0

Therefore, either (2·x - 3) = 0 and x = 3/2 or (3·x - 2) = 0 and x = 2/3

From which we have 6·x² - 13·x + 6 = 0 when x = 3/2 or 2/3 and x = 3/2 or x = 2/3 are the solution of the equation 6·x² - 13·x + 6 = 0.

problem:

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

f(5/2) = 10/3

i hope this !

a precentage of 6th graders. the population is all 6th graders. let me know if i'm wrong, i hope this ! : )

step-by-step explanation: