Question

the sum of the roots of a quadratic equation. is 7 and the sum of their cubes is 133. to find the quadratic equation, fill in the empty boxes. ​

Answer 1

Answer:

Given x +y= 7

X cube+ycube=133

We know (x+y)^3=x^3+y^3+3xy(x+y)

Substituting the given, equation becomes

7^3=133+3xy(7)

343=133+21xy

Hence xy=10

We know (x+y)^2=x^2+y^2+2xy

Substitute values of x+y and xy

7^2=x^2+y^2+20

49–20= x^2+y^2

Hence sum of their squares is 29

Step-by-step explanation:

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Answer 2

Given :-

• x + y = 7
• x³ + y³ = 133

To Find :-

• The quadratic equation

Solution :-

x + y = 7

x³ + y³ = 133

Now,

(x+y)³ = x³ + y³ + 3xy(x+y)

=> 7³ = 133 + 3xy(7)

=> 343 = 133 + 3xy(7)

=> 343 - 133 = 21xy

=> 210 = 21xy

=> xy = 210/21

=> xy = 10

Now,

Sum of Zeroes = x + y = 7

Product of Zeroes = xy = 10

Putting the value in the equation below we get,

x² + (Sum of zeroes) x + (product of Zeroes)

=> x² + ( x + y ) x + (xy)

=> x² + (7)x + (10)

=> x² + 7x + 10

∴ x² + 7x + 10 is the required answer .