If f(x) = 2x^3 + mx^2 - 13x + n and 2, 3 are | vedclass

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(B) Given $f(x) = 2x^3 + mx^2 - 13x + n$. Since $2$ and $3$ are roots of $f(x) = 0$,we have $f(2) = 0$ and $f(3) = 0$. For $f(2) = 0$: $2(2)^3 + m(2)^

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$-5, 30$

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(B) Given $f(x) = 2x^3 + mx^2 - 13x + n$. Since $2$ and $3$ are roots of $f(x) = 0$,we have $f(2) = 0$ and $f(3) = 0$. For $f(2) = 0$: $2(2)^3 + m(2)^2 - 13(2) + n = 0$ $\Rightarrow 16 + 4m - 26 + n = 0$ $\Rightarrow 4m + n = 10 \dots (i)$. For $f(3) = 0$: $2(3)^3 + m(3)^2 - 13(3) + n = 0$ $\Rightarrow 54 + 9m - 39 + n = 0$ $\Rightarrow 9m + n = -15 \dots (ii)$. Subtracting equation $(i)$ from $(ii)$: $(9m + n) - (4m + n) = -15 - 10$ $\Rightarrow 5m = -25$ $\Rightarrow m = -5$. Substituting $m = -5$ into equation $(i)$: $4(-5) + n = 10$ $\Rightarrow -20 + n = 10$ $\Rightarrow n = 30$. Thus,the values are $m = -5$ and $n = 30$.

If $f(x) = 2x^3 + mx^2 - 13x + n$ and $2, 3$ are roots of the equation $f(x) = 0$,then the values of $m$ and $n$ are $-$

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