5x2-24x-5=0 find the roots
Answers
Answer:
Step-by-step explanation:
2.1 Factoring 5x2-24x-5
The first term is, 5x2 its coefficient is 5 .
The middle term is, -24x its coefficient is -24 .
The last term, "the constant", is -5
Step-1 : Multiply the coefficient of the first term by the constant 5 • -5 = -25
Step-2 : Find two factors of -25 whose sum equals the coefficient of the middle term, which is -24 .
-25 + 1 = -24 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -25 and 1
5x2 - 25x + 1x - 5
Step-4 : Add up the first 2 terms, pulling out like factors :
5x • (x-5)
Add up the last 2 terms, pulling out common factors :
1 • (x-5)
Step-5 : Add up the four terms of step 4 :
(5x+1) • (x-5)
Which is the desired factorization
Equation at the end of step
2
:
(x - 5) • (5x + 1) = 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 : x-5 = 0
Add 5 to both sides of the equation :
x = 5
Solving a Single Variable Equation:
3.3 Solve : 5x+1 = 0
Subtract 1 from both sides of the equation :
5x = -1
Divide both sides of the equation by 5:
x = -1/5 = -0.200
Supplement : Solving Quadratic Equation Directly
Solving 5x2-24x-5 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula