Question

if (alpha-beta),a,(alpha + beta)are the zeros of the polynomial 2x^3-16x^2+15x-2,then the value of alpha is
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Answer 1

Answer:

$\alpha = \dfrac{8}{3}$

Step-by-step explanation:

The given equation is-

$2x^{3} -16x^{2} + 15x - 2 = 0$

Comparing the equation with-

$ax^{3}+bx^{2}+cx+d= 0$

We have-

a = 2, b = -16, c = 15 and d = -2

Given that-

(α - β), α and (α + β) are the three roots of the given equation.

We know that-

Sum of roots of the equation = $-\dfrac{b}{a}$

$(\alpha - \beta) + \alpha   +(\alpha +\beta ) = -\dfrac{(-16)}{2}$

$3\alpha = 8$

$\alpha = \dfrac{8}{3}$