Math, asked by abhinav2590, 1 year ago

find the zeros of the polynomial 4x2+13x+9

Answers

Answered by aranya1045
0
4x2+(9+4)x+9=0
4x2+9x+4x+9=0
(4x2+9x)+(4x+9)=0
x(4x+9)+1(4x+9)=0
(4x+9) (x+1)=0
if 4x+9=0 then 4x=-9
x= -9÷4
again x+1 =0
then x=-1
the two zeros are
-9÷4 and-1
hope it will help you
Answered by umasubafs
0

The first term is,  4x2  its coefficient is  4 .

The middle term is,  -13x  its coefficient is  -13 .

The last term, "the constant", is  +9  

Step-1 : Multiply the coefficient of the first term by the constant   4 • 9 = 36  

Step-2 : Find two factors of  36  whose sum equals the coefficient of the middle term, which is   -13 .

     -36    +    -1    =    -37  

     -18    +    -2    =    -20  

     -12    +    -3    =    -15  

     -9    +    -4    =    -13    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -9  and  -4  

                    4x2 - 9x - 4x - 9

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (4x-9)

             Add up the last 2 terms, pulling out common factors :

                    1 • (4x-9)

Step-5 : Add up the four terms of step 4 :

                   (x-1)  •  (4x-9)

            Which is the desired factorization

Equation at the end of step  2  :

 (4x - 9) • (x - 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  :    4x-9 = 0  

Add  9  to both sides of the equation :  

                     4x = 9  

Divide both sides of the equation by 4:

                    x = 9/4 = 2.250  

Solving a Single Variable Equation :

3.3      Solve  :    x-1 = 0  

Add  1  to both sides of the equation :  

                     x = 1  

Supplement : Solving Quadratic Equation Directly

Solving    4x2-13x+9  = 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

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