Question

the quadratic equation for which the sum of the root is 12 and the sum of cubes of the roots is 468 is​

Answer 1

Answer:

x²-12x+35=0

Step-by-step explanation:

Given,

Sum of the roots is 12 and sum of the cubes of roots is 468.

To Find,

The quadratic equation satisfying it.

Let x and y be the roots, S be the sum of roots and P be the product.

So, the equation is x²-Sx+P=0

Now,

x+y = 12

x³+y³ = 468

Cubing the sum of the roots we get:

(x+y)³ = 12³

⇒ x³+y³+3xy (x+y) = 1728

Substituting the value of x³+y³ as 468

⇒ 468 + 3xy (12) = 1728

⇒ 36xy = 1260

⇒ xy = 35

Now, since we know the sum and the product of the roots we can form the equation as:

x²-12x+35=0

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