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2 years ago

Write the quadratic equation that has roots (-1-√2)/3 and (-1+√2)/3 , if it's coefficient with x^2 is equal to

Mathematics

1 answer:

MArishka [77]2 years ago

3 0

9514 1404 393

Answer:

(a) x² +2/3x -1/9 = 0

(b) 9x² +6x -1 = 0

Step-by-step explanation:

The product of quadratic factors can be expanded to give ...

(x -p)(x -q) = x² -(p+q)x +pq

Then the coefficients of x² +bx +c = 0 will be ...

b = -((-1-√2)/3 +(-1+√2)/3)) = 2/3

c = ((-1-√2)/3)·((-1+√2)/3) = (-1/3)² -(√2/3)²) = 1/9 -2/9 = -1/9

a) The quadratic with leading coefficient 1 is ...

x² +2/3x -1/9 = 0

b) Multiplying that by 9 gives ...

9x² +6x -1 = 0

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