Find the roots of the function f(x)=(2x-1)\times(x^{2}+2x-3) with x\in R

b2sonicxh

b2sonicxh

Answered question

2021-12-16

Find the roots of the function f(x)=(2x1)×(x2+2x3) with xR

Answer & Explanation

Jimmy Macias

Jimmy Macias

Beginner2021-12-17Added 30 answers

Step 1
Consider the given function,
f(x)=(2x1)×(x2+2x3)
First find the factors of
(x2+2x3)
Compare the ax2+bx+c and x2+2x3, implies that a=1, b=2, and c=3
The ac-method of factoring quadratics: To find factors of quadratic ax2+bx+c. Find two numbers whose sum is b and product is a×c
Here a×c=1×(3)=3 and b=2
To find factors of quadratic x2+2x3, find two numbers whose sum is 2 and the product is -3.
Such numbers are 3 and -1.
The factors of (x2+2x3) are (x+3)(x1)
Step 2
The given function f(x)=(2x1)×(x2+2x3) becomes
f(x)=(2x1)×(x+3)×(x1)
Set f(x)=0, inplies that
(2x1)×(x+3)×(x1)=0
By using zero product property,
(2x1)=0, (x+3)=0, (x1)=0
Implies that,
2x=1, x=3, x=1
That is, roots of the given function are,
x=12, x=3, x=1
reinosodairyshm

reinosodairyshm

Beginner2021-12-18Added 36 answers

Step 1
f(x)=(2x1)×(x2+2x3)
(2x1)(x2+2x3)=0
(2x1)(x+3)(x1)=0
table
2x=1x=3x=1x=log21x=3x=1x=0x=3x=1
2x1=0
2x=1=20
x=0
Don Sumner

Don Sumner

Skilled2021-12-28Added 184 answers

Step 1
Given: f(x)=(2x1)×(x2+2x3)
=(2x1)×(x+3)×(x1)
So if the root should be
2x-1=0
or
x+3=0
or
x-1=0,
so
2x=1
or
x=-3 or x=1
2x=1, x=0
so x=0 or -3 or 1

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