Question

factories a3-2a-4 =0​

Answer 1

Answer:

8 sahi hai i don no batao sahhi

Answer 2

Find roots (zeroes) of :       F(a) = a3-2a-4

Polynomial Roots Calculator is a set of methods aimed at finding values of  a  for which   F(a)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  a  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  1  and the Trailing Constant is  -4.

 The factor(s) are:

of the Leading Coefficient :  1

 of the Trailing Constant :  1 ,2 ,4

 Let us test ....  P  Q  P/Q  F(P/Q)   Divisor     -1     1      -1.00      -3.00        -2     1      -2.00      -8.00        -4     1      -4.00      -60.00        1     1      1.00      -5.00        2     1      2.00      0.00    a-2      4     1      4.00      52.00   

The Factor Theorem states that if P/Q is root of a polynomial then this polynomial can be divided by q*x-p Note that q and p originate from P/Q reduced to its lowest terms

In our case this means that

   a3-2a-4 

can be divided with  a-2 

Polynomial Long Division :

 1.2    Polynomial Long Division

Dividing :  a3-2a-4 

                              ("Dividend")

By         :    a-2    ("Divisor")

dividend  a3   - 2a - 4 - divisor * a2   a3 - 2a2     remainder    2a2 - 2a - 4 - divisor * 2a1     2a2 - 4a   remainder      2a - 4 - divisor * 2a0       2a - 4 remainder       0

Quotient :  a2+2a+2  Remainder:  0 

Trying to factor by splitting the middle term

 1.3     Factoring  a2+2a+2 

The first term is,  a2  its coefficient is  1 .

The middle term is,  +2a  its coefficient is  2 .

The last term, "the constant", is  +2 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 2 = 2 

Step-2 : Find two factors of  2  whose sum equals the coefficient of the middle term, which is   2 .

     -2   +   -1   =   -3     -1   +   -2   =   -3     1   +   2   =   3     2   +   1   =   3

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step1:

(a2 + 2a + 2) • (a - 2) = 0

STEP2: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.