If the cubic equation \(a^3 - 4a^2 + 5a - 2 = 0\) has the roots x, y, z then find the value of x + y + z.
4
For a cubic equation \(a^3 + pa^2 + qa + r = 0\), the sum of roots is \(-p\) (Vieta's formula).
Here the equation is \(a^3 - 4a^2 + 5a - 2 = 0\), so \(p = -4\).
\(x + y + z = -(-4) = \mathbf{{4}}\)
Important Questions from Polynomials
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If (x 2- 1) is a factor of ax 4+ bx 3+ cx 2+ dx + e, then which one of the following is correct?
If (x + 1) and (x - 2) are the factors of the polynomial p(x) = x 3- ax 2+ bx + 6, then the respective values of a and b are:
