find the integral zeros of 4x³+20x²-x-5
Answers
Answer:
e steps
Step by Step Solution

Step by step solution :
STEP1:Equation at the end of step 1
(((4 • (x3)) - (22•5x2)) + x) - 5 = 0
STEP 2 :
Equation at the end of step2:
((22x3 - (22•5x2)) + x) - 5 = 0
STEP3:Checking for a perfect cube
3.1 4x3-20x2+x-5 is not a perfect cube
Trying to factor by pulling out :
3.2 Factoring: 4x3-20x2+x-5
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: x-5
Group 2: 4x3-20x2
Pull out from each group separately :
Group 1: (x-5) • (1)
Group 2: (x-5) • (4x2)
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Add up the two groups :
(x-5) • (4x2+1)
Which is the desired factorization
Polynomial Roots Calculator :
3.3 Find roots (zeroes) of : F(x) = 4x2+1
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 4 and the Trailing Constant is 1.
The factor(s) are:
of the Leading Coefficient : 1,2 ,4
of the Trailing Constant : 1
Let us test .... P Q P/Q F(P/Q) Divisor -1 1 -1.00 5.00 -1 2 -0.50 2.00 -1 4 -0.25 1.25 1 1 1.00 5.00 1 2 0.50 2.00 1 4 0.25 1.25
Polynomial Roots Calculator found no rational roots
Equation at the end of step3:
(4x2 + 1) • (x - 5) = 0
STEP4:Theory - Roots of a product
4.1 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:
4.2 Solve : 4x2+1 = 0
Subtract 1 from both sides of the equation :
4x2 = -1
Divide both sides of the equation by 4:
x2 = -1/4 = -0.250
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
x = ± √ -1/4
In Math, i is called the imaginary unit. It satisfies i2 =-1. Both i and -i are the square roots of -1
Accordingly, √ -1/4 =
√ -1• 1/4 =
√ -1 •√ 1/4 =
i • √ 1/4
The equation has no real solutions. It has 2 imaginary, or complex solutions.
x= 0.0000 + 0.5000 i
x= 0.0000 - 0.5000 i
Solving a Single Variable Equation:
4.3 Solve : x-5 = 0
Add 5 to both sides of the equation :
x = 5
Three solutions were found :
x = 5
x= 0.0000 - 0.5000 i
x= 0.0000 + 0.5000 i
Step-by-step explanation:
I hope its help you
your answer is in the above picture
and one more thing! in my notebook there is y instead of x.. but the question is all same!
hope it helps...
