find the sum and the product of the following equations?find the sum and the product of the following equations:a.) 2x^2-8x+5=0b.)3x^2-9x=0c.)-.5 (in fraction form)x^2-3x+2=0

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giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

The sum and the product are:

x1 + x2 = S

x1*x2 = P

We'll use Viete's relations to calculate the sum and the product:

x1 + x2 = -b/a

x1*x2 = c/a

a,b,c are the coefficients of the given equations.

a.) 2x^2-8x+5=0

We'll identify a,b,c:

a = 2 , b = -8 , c = 5

x1 + x2 = -(-8)/2

x1 + x2 = 4

x1*x2 = 5/2

The sum S = 4 and the product is P = 5/2.


b.) 3x^2-9x=0

We'll identify a,b,c:

a = 3, b =-9 , c = 0

x1 + x2 = -(-9/3)

S = 3

x1*x2 = 0/3

P = 0

The sum S = 3 and the product is P = 0.


c.)x^2-3x+2=0

We'll identify a,b,c:

a = 1 , b = -3 , c = 2

x1 + x2 = 3

x1*x2 = 2

The sum S = 3 and the product is P = 2.

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neela | High School Teacher | (Level 3) Valedictorian

Posted on

Hope it is the sum product of the roots:

We know that if ax^2+bx +c = 0 , and the roots x1 and x2, then

the sum of roots is x1+x2 = -b/a and  the product of the roots is x1x2 = c/a. We apply this to the given equations:

a.) 2x^2-8x+5=0'

Here identify a= 2, b = -8 and c = 5.

Sum x1+x1 = - (-8/2) = 4 and product of roots x1x2 = 5/2 = 2.5.


b.)3x^2-9x=0.

Here a = 3, b= -9.  c = 0 ( c is absent.)

So sum of the roots x1+x2  = -(-9/3) = 3

Product of the roots x1x2 = 0/3 = 0.


c.)-.5 (in fraction form)x^2-3x+2=0

 a = -0.5 . b = -3 and c = -2.

Therefore sum of the roots = x1+x2 = -(-3/-0.5) = -6/

Product of the roots = x1x2 = -2/-0.5 = 4.

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