Question

If -2 and 5 are the root of equation 2x^2 -3mx +5n =0,then find value Of m and n.

Answer 1

this is the answer

m=2 and n=-4

Answer 2

$Given \: -2\: and \: 5 \: are \:the \: root \: of$

$2x^{2} - 3mx+5n = 0$

/* put x =-2 in the equation ,we get */

$\implies 2(-2)^{2} - 3m(-2) + 5n = 0$

$\implies 8 + 6m + 5n = 0\: ---(1)$

/* put x = 5 in the equation ,we get */

$\implies 2\times (5)^{2} - 3m\times 5 + 5n = 0$

$\implies 50 - 15m + 5n = 0\: ---(2)$

/* Subtract equation (2) from Equation (1), we get */

$- 42 + 21m = 0$

$\implies 21 m = 42$

$\implies m = \frac{42}{21}$

$\implies m = 2$

/* put m = 2 in equation (1) , we get */

$8 + 6\times 2 + 5n = 0$

$\implies 8 + 12 + 5n = 0$

$\implies 20 + 5n = 0$

$\implies 5n = -20$

$\implies n = \frac{-20}{5}$

$\implies n = -4$

Therefore.,

$\red{ Value \: m } \green { = 2}$

$\red{ Value \: n } \green { = -4}$

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