if the equation x^4 - x^3 + ax^2 + bx + 1 = 0 has four positive roots then find the value of a and b?

Answer 1

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four positive roots means 4 sign changes.

so a>0 and b<0.

Answer 2

If the equation x^4 - x^3 + ax^2 + bx + 1 = 0 has four positive roots, it can be written as:

(x - c)(x - d)(x - e)(x - f) = 0, where c,d,e,f are the roots.

(x - c)(x - d)(x - e)(x - f) = x^4 - x^3 + ax^2 + bx + 1

multiply it out and compare coefficients (i.e. you get c^2d+e on the left side with x^4 ==> c^2d+e = 1, etc.)

From those equations you should be able to find a and b.