Let r_1, r_2, r_3 be the roots of the equatio | vedclass

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(B) Let $P(x) = x^3 - 2x^2 + 4x + 5074$. Since $r_1, r_2, r_3$ are the roots of $P(x) = 0$,we can write the polynomial as:$P(x) = (x - r_1)(x - r_2)(x

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$-5050$

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(B) Let $P(x) = x^3 - 2x^2 + 4x + 5074$. Since $r_1, r_2, r_3$ are the roots of $P(x) = 0$,we can write the polynomial as:$P(x) = (x - r_1)(x - r_2)(x - r_3)$We want to find the value of $(r_1 + 2)(r_2 + 2)(r_3 + 2)$.Notice that $(r_1 + 2)(r_2 + 2)(r_3 + 2) = -(-r_1 - 2)(-r_2 - 2)(-r_3 - 2) = -((-2 - r_1)(-2 - r_2)(-2 - r_3))$.Alternatively,consider $P(-2)$:$P(-2) = (-2 - r_1)(-2 - r_2)(-2 - r_3) = (-1)^3 (2 + r_1)(2 + r_2)(2 + r_3) = -(r_1 + 2)(r_2 + 2)(r_3 + 2)$.Now,calculate $P(-2)$ using the given equation:$P(-2) = (-2)^3 - 2(-2)^2 + 4(-2) + 5074$$P(-2) = -8 - 2(4) - 8 + 5074$$P(-2) = -8 - 8 - 8 + 5074 = -24 + 5074 = 5050$.Since $P(-2) = -(r_1 + 2)(r_2 + 2)(r_3 + 2)$,we have:$5050 = -(r_1 + 2)(r_2 + 2)(r_3 + 2)$Therefore,$(r_1 + 2)(r_2 + 2)(r_3 + 2) = -5050$.

Let $r_1, r_2, r_3$ be the roots of the equation $x^3 - 2x^2 + 4x + 5074 = 0$. Then the value of $(r_1 + 2)(r_2 + 2)(r_3 + 2)$ is:

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