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