if the product of two roots of the equation 4x^4-24x^3+31x^2+6x-8=0 is 1, then the possability of sum of two zeroes are
Answers
Step-by-step explanation:
4x4-24x3+31x2-6x-8=0
One solution was found :
x ≓ -0.376139224
Step by step solution :
Step 1 :
Equation at the end of step 1 :
((((4•(x4))-(24•(x3)))+31x2)-6x)-8 = 0
Step 2 :
Equation at the end of step 2 :
((((4•(x4))-(23•3x3))+31x2)-6x)-8 = 0
Step 3 :
Equation at the end of step 3 :
(((22x4 - (23•3x3)) + 31x2) - 6x) - 8 = 0
Step 4 :
Polynomial Roots Calculator :
4.1 Find roots (zeroes) of : F(x) = 4x4-24x3+31x2-6x-8
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 -8.
The factor(s) are:
of the Leading Coefficient : 1,2 ,4
of the Trailing Constant : 1 ,2 ,4 ,8
Given : 4x⁴-24x³+31x²+ 6x-8=0
To find : possibility of sum of two zeroes
Solution:
4x⁴-24x³+31x²+ 6x-8=0
x = 2 will give zero
=> (x - 2) is a root
=> 4x⁴-24x³+31x²+ 6x-8 = (x - 2) (4x³ - 16x² - x + 4)
= (x - 2)(2x - 1)(2x² - 7x - 4)
= (x - 2)(2x - 1)(2x² - 8x + x - 4)
= (x - 2)(2x - 1)(2x(x - 4) + 1(x - 4))
= (x - 2)(2x - 1)(2x + 1)(x - 4)
Zeroes are
- 1/2 , 1/2 , 2 , 4
2(1/2) = 1
2 + 1/2 = 5/2
Taking all pairs
- 1/2 + 1/2 = 0 , -1/2 + 2 = 3/2 , -1/2 + 4 = 7/2
1/2 + 2 = 5/2 , 1/2 + 4 = 9/2
2 + 4 = 6
Possible sum of Zeroes = 0 , 3/2 , 5/2 , 7/2 , 9/2 , 6
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