This deals with finding the roots (zeroes) of polynomials.
Overview
Steps
3 solution(s) found
See steps
Step by Step Solution

Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2". 1 more similar replacement(s).
Step by step solution :
STEP1:Equation at the end of step 1
(((2 • (x3)) - (22•3x2)) + 13x) - 15 = 0
STEP 2 :
Equation at the end of step2:
((2x3 - (22•3x2)) + 13x) - 15 = 0
STEP3:Checking for a perfect cube
3.1 2x3-12x2+13x-15 is not a perfect cube
Trying to factor by pulling out :
3.2 Factoring: 2x3-12x2+13x-15
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 13x-15
Group 2: 2x3-12x2
Pull out from each group separately :
Group 1: (13x-15) • (1)
Group 2: (x-6) • (2x2)
Bad news !! Factoring by pulling out fails :
The groups have no common factor and can not be added up to form a multiplication.
Polynomial Roots Calculator :
3.3 Find roots (zeroes) of : F(x) = 2x3-12x2+13x-15
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x 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 2 and the Trailing Constant is -15.
The factor(s) are:
of the Leading Coefficient : 1,2
of the Trailing Constant : 1 ,3 ,5 ,15
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
Answers & Comments
Answer :
x=(2+sqrt(-20))/4=(1+isqrt(5))/2=0.5000+1.1180i
Step-by-step explanation:
2x3−12x2+13x−15=0
This deals with finding the roots (zeroes) of polynomials.
Overview
Steps
3 solution(s) found
See steps
Step by Step Solution

Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2". 1 more similar replacement(s).
Step by step solution :
STEP1:Equation at the end of step 1
(((2 • (x3)) - (22•3x2)) + 13x) - 15 = 0
STEP 2 :
Equation at the end of step2:
((2x3 - (22•3x2)) + 13x) - 15 = 0
STEP3:Checking for a perfect cube
3.1 2x3-12x2+13x-15 is not a perfect cube
Trying to factor by pulling out :
3.2 Factoring: 2x3-12x2+13x-15
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: 13x-15
Group 2: 2x3-12x2
Pull out from each group separately :
Group 1: (13x-15) • (1)
Group 2: (x-6) • (2x2)
Bad news !! Factoring by pulling out fails :
The groups have no common factor and can not be added up to form a multiplication.
Polynomial Roots Calculator :
3.3 Find roots (zeroes) of : F(x) = 2x3-12x2+13x-15
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x 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 2 and the Trailing Constant is -15.
The factor(s) are:
of the Leading Coefficient : 1,2
of the Trailing Constant : 1 ,3 ,5 ,15
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
2x3-12x2+13x-15
can be divided with x-5
Polynomial Long Division :
3.4 Polynomial Long Division
+Dividing : 2x3-12x2+13x-15
("Dividend")
By : x-5 ("Divisor")
dividend 2x3 - 12x2 + 13x - 15 - divisor * 2x2 2x3 - 10x2 remainder - 2x2 + 13x - 15 - divisor * -2x1 - 2x2 + 10x remainder 3x - 15 - divisor * 3x0 3x - 15 remainder 0
Quotient : 2x2-2x+3 Remainder: 0
Trying to factor by splitting the middle term
3.5 Factoring 2x2-2x+3
The first term is, 2x2 its coefficient is 2 .
The middle term is, -2x its coefficient is -2 .
The last term, "the constant", is +3
Step-1 : Multiply the coefficient of the first term by the constant 2 • 3 = 6
correct me if I'm Wrong,
I hoped it helps and pa Brainliest please