SOLUTION: Please l need your help for this assignment.if a and b are the root of the quadratic equation 3x³-4x-7=0, find a²/B +B²/a

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Question 1196712: Please l need your help for this assignment.if a and b are the root of the quadratic equation 3x³-4x-7=0, find a²/B +B²/a
Found 4 solutions by greenestamps, ikleyn, MathTherapy, math_tutor2020:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


Don't mix upper case and lower case letters when naming your variables. "b" and "B" in the same problem can represent completely different quantities.

We are to evaluate the expression



which, combining the fractions with a common denominator, is equivalent to



We can work this problem using Vieta's Theorem which says the sum of the roots is and the product of the roots is



Use the factorization pattern for the sum of cubes:



Since we know the values of a+b and ab, rewrite the other term as



Then the expression we are to evaluate is all in terms of (a+b) and (ab):



Substitute and and evaluate.











ANSWER:


Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
.
Please l need your help for this assignment.
If a and b are the root of the quadratic equation 3x³-4x-7=0, find a²/b +b²/a.
~~~~~~~~~~~~~~~~ 

From the given part, we have, due to Vieta's formulas

    a + b = ;  a*b = .     (1)


From the other side,

     +  = .    (2)


The numerator is 

     =  =  = 

            =  = now substitute from (1) =  = 

            =  =  =  =  = .


Now we can continue and complete (2) in this way

     +  =  =  = -  = -  = -5.    ANSWER

Solved.



Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Please l need your help for this assignment.if a and b are the root of the quadratic equation 3x³-4x-7=0, find a²/B +B²/a
              
x(3x - 7) + 1(3x - 7) = 0
 x + 1 = 0     and      3x - 7 = 0, and so, roots, or 

                                                   

Switching the variables  yields the same result.
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

I think you meant to say 3x^2-4x-7 = 0 instead of 3x^3-4x-7 = 0

Compare 3x^2-4x-7 = 0 to ax^2+bx+c=0
to find that
a = 3, b = -4, c = -7
These a,b values are NOT the roots mentioned
I wish your teacher used p,q for the roots (or anything else except for a,b)

Anyways this is what the steps look like for the quadratic formula.








or

or

or
The two roots are p = 7/3 and q = -1
The order of the roots doesn't matter.

We're asked to compute where p,q are the roots of 3x^2-4x-7 = 0

















Therefore,

when p = 7/3 and q = -1, which are the roots of 3x^2-4x-7 = 0
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