Answer Show Hint: In order to determine solution of the above quadratic question use the Splitting up the middle method by first multiplying the coefficient of $ {x^2} $ with the constant term and factorise it into two factors such that either addition or subtraction gives us the middle term and the product of the same gives us back the multiplication we have calculated. Pull out common from the first two terms and the last two terms and then again pull out the common binomial parenthesis to get your required answer. Complete step-by-step solution: Note: Rearrange:Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 3*x^2-8*x-(5)=0 Step by step solution :Step 1 :Equation at the end of step 1 : (3x2 - 8x) - 5 = 0
Step 2 :Trying to factor by splitting the middle term2.1 Factoring 3x2-8x-5 The first term is, 3x2 its coefficient is 3 . Step-1 : Multiply the coefficient of the first term by the constant 3 • -5 = -15 Step-2 : Find two factors of -15 whose sum equals the coefficient of the middle term, which is -8 .
Equation at the end of step 2 : 3x2 - 8x - 5 = 0
Step 3 :Parabola, Finding the Vertex : 3.1 Find the Vertex of y = 3x2-8x-5Parabolas have a highest or a
lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 3 , is positive (greater than zero). Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would,
for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions. Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to
find the coordinates of the vertex. For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 1.3333 Plugging into the parabola formula 1.3333 for x we can calculate the y -coordinate : Parabola, Graphing Vertex and X-Intercepts :Root plot for : y = 3x2-8x-5 Solve Quadratic Equation by Completing The Square 3.2 Solving 3x2-8x-5 = 0 by Completing The Square .Divide both sides of the equation by 3 to have 1 as the coefficient of the first term : Add 5/3 to both side of the equation : Now the clever bit: Take the coefficient of x , which is 8/3 , divide by two, giving 4/3 , and finally square it giving 16/9 Add 16/9 to both sides of
the equation : Adding 16/9
has completed the left hand side into a perfect square : We'll refer to this Equation as Eq. #3.2.1 The Square Root Principle says that When two things are equal, their square roots are equal. Note that the square root of Now, applying the Square Root Principle to Eq. #3.2.1 we get: Add 4/3 to both sides to obtain: Since a square root has two values, one positive and the other negative Note that √ 31/9 can be written as Solve Quadratic Equation using the Quadratic Formula 3.3 Solving 3x2-8x-5 = 0 by the Quadratic Formula .According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are
numbers, often called coefficients, is given by : 8 ± √ 124 Yes! The prime factorization of 124 is √ 124 = √ 2•2•31
= √ 31 , rounded to 4 decimal digits, is 5.5678 Two real solutions: x =(8+√124)/6=(4+√ 31 )/3= 3.189 or: x =(8-√124)/6=(4-√ 31 )/3= -0.523 Two solutions were found :
Which of the following is a zero of the polynomial 3x² 8x 5?We divide b into two parts whose sum is equal to b and its product is equal to ac. Answer: Step-by-step explanation: Hence zero of the polynomial is 1.
What is the other factor of 3x 2 10x 8?Thus the other factor of 3x2 - 10x + 8 is (x - 2).
What is factorization form?A fully factored form means the given number or polynomial is expressed as a product of the simplest possible form. For example, if we write 12y2−27=3(4y2−9) 12 y 2 − 27 = 3 ( 4 y 2 − 9 ) , then it is not considered as fully factored form as (4y2−9) ( 4 y 2 − 9 ) can be factored further.
What are the factors of x2 100?What are the factors of x2- 100? Summary: By solving the given quadratic equation x2 - 100 with factorising method we get the two linear factors as(x + 10) and (x - 10) .
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