factorise z²-10z+21=0
Answers
Step-by-step explanation:
z2+10z+21=0
Two solutions were found :
z = -3
z = -7
Step by step solution :
Step 1 :
Trying to factor by splitting the middle term
1.1 Factoring z2+10z+21
The first term is, z2 its coefficient is 1 .
The middle term is, +10z its coefficient is 10 .
The last term, "the constant", is +21
Step-1 : Multiply the coefficient of the first term by the constant 1 • 21 = 21
Step-2 : Find two factors of 21 whose sum equals the coefficient of the middle term, which is 10 .
-21 + -1 = -22 -7 + -3 = -10 -3 + -7 = -10 -1 + -21 = -22 1 + 21 = 22 3 + 7 = 10 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 3 and 7
z2 + 3z + 7z + 21
Step-4 : Add up the first 2 terms, pulling out like factors :
z • (z+3)
Add up the last 2 terms, pulling out common factors :
7 • (z+3)
Step-5 : Add up the four terms of step 4 :
(z+7) • (z+3)
Which is the desired factorization
Equation at the end of step 1 :
(z + 7) • (z + 3) = 0
Step 2 :
Theory - Roots of a product :
2.1 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 :
2.2 Solve : z+7 = 0
Subtract 7 from both sides of the equation :
z = -7
Solving a Single Variable Equation :
2.3 Solve : z+3 = 0
Subtract 3 from both sides of the equation :
z = -3
Supplement : Solving Quadratic Equation Directly
Answer: