Solve the following equations by factorisation:
(i) x2 + 4x – 12 = 0
(ii) 5x2 + 11x + 6 = 0
(iii) 9x2 – 17x + 8 = 0
(iv) 36x2 – 60x + 25 = 0
Answers
Step-by-step explanation:
please mark me as brainliest answerChanges made to your input should not affect the solution:
(1): "x2" was replaced by "x^2".
Step by step solution :
STEP
1
:
Equation at the end of step 1
((0 - 5x2) + 11x) - 6 = 0
STEP
2
:
STEP
3
:
Pulling out like terms
3.1 Pull out like factors :
-5x2 + 11x - 6 = -1 • (5x2 - 11x + 6)
Trying to factor by splitting the middle term
3.2 Factoring 5x2 - 11x + 6
The first term is, 5x2 its coefficient is 5 .
The middle term is, -11x its coefficient is -11 .
The last term, "the constant", is +6
Step-1 : Multiply the coefficient of the first term by the constant 5 • 6 = 30
Step-2 : Find two factors of 30 whose sum equals the coefficient of the middle term, which is -11 .
-30 + -1 = -31
-15 + -2 = -17
-10 + -3 = -13
-6 + -5 = -11 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and -5
5x2 - 6x - 5x - 6
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (5x-6)
Add up the last 2 terms, pulling out common factors :
1 • (5x-6)
Step-5 : Add up the four terms of step 4 :
(x-1) • (5x-6)
Which is the desired factorization
Equation at the end of step
3
:
(6 - 5x) • (x - 1) = 0
STEP
4
:
Theory - Roots of a product
4.1 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:
4.2 Solve : -5x+6 = 0
Subtract 6 from both sides of the equation :
-5x = -6
Multiply both sides of the equation by (-1) : 5x = 6
Divide both sides of the equation by 5:
x = 6/5 = 1.200
Answer:
142241148
Step-by-step explanation:
2=62765458727426÷654