Question

if the zeros of the polynomial x cube minus 3 X square + X + 1 hour a minus b, a, a + b, find a and​

Answer 1

Answer:

   a = 1  and  b = ±√2.

   The roots are 1,  1-√2  and  1+√2.

Step-by-step explanation:

For a cubic

   Ax³ + Bx² + Cx + D

the sum of the roots is -B/A and the product of the roots is -D/A.

So for the cubic

   x³ - 3x² + x + 1

the sum of the roots is 3 and the product of the roots is -1.

As the roots are a-b, a and a+b, the sum is then

    (a-b) + a + (a+b) = 3

⇒  3a = 3

⇒  a = 1.

The product of the roots is

    (a-b)a(a+b) = -1

⇒  (1-b)(1+b) = -1

⇒  1 - b² = -1

⇒  b² = 2

⇒  b = ±√2.

It follows that the three roots are

   1,  1 - √2  and  1 + √2.

Hope this helps.

Answer 2

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