Find the root of 6y-5y square =0
By factorisation
Answers
hey m8,
6y2-5y-6=0
Two solutions were found :
y = -2/3 = -0.667
y = 3/2 = 1.500
Step by step solution :
Step 1 :
Equation at the end of step 1 :
((2•3y2) - 5y) - 6 = 0
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 6y2-5y-6
The first term is, 6y2 its coefficient is 6 .
The middle term is, -5y its coefficient is -5 .
The last term, "the constant", is -6
Step-1 : Multiply the coefficient of the first term by the constant 6 • -6 = -36
Step-2 : Find two factors of -36 whose sum equals the coefficient of the middle term, which is -5 .
-36 + 1 = -35
-18 + 2 = -16
-12 + 3 = -9
-9 + 4 = -5 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -9 and 4
6y2 - 9y + 4y - 6
Step-4 : Add up the first 2 terms, pulling out like factors :
3y • (2y-3)
Add up the last 2 terms, pulling out common factors :
2 • (2y-3)
Step-5 : Add up the four terms of step 4 :
(3y+2) • (2y-3)
Which is the desired factorization
Equation at the end of step 2 :
(2y - 3) • (3y + 2) = 0
Step 3 :
Theory - Roots of a product :
3.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation :
3.2 Solve : 2y-3 = 0
Add 3 to both sides of the equation :
2y = 3
Divide both sides of the equation by 2:
y = 3/2 = 1.500
Solving a Single Variable Equation :
3.3 Solve : 3y+2 = 0
Subtract 2 from both sides of the equation :
3y = -2
Divide both sides of the equation by 3:
y = -2/3 = -0.667