Find the roots of the function f(x) = (2x − 1)*(x^2 + 2x − 3), with x in R

rocedwrp 2021-03-08 Answered
Find the roots of the function
f(x)=(2x1)(x2+2x3), with xR
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Expert Answer

StrycharzT
Answered 2021-03-09 Author has 102 answers

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 ac.
Here ac=1(3)=3and 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).
The given function f(x)=(2x1)(x2+2x3) becomes
f(x)=(2x1)·(x+3)·(x1)
Set f(x)=0, implies 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, the roots of the given function are,
x=12,x=3,x=1.

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