Question

if root 2/3 is a solution of equation 3x^2 + mx +2=0 . find value of m

Answer 1

3x²+mx+2=0

3(√2/3)²+m(√2/3)+2=0

2+m(√2/3)+2=0

m(√2/3)=-4

squaring both side, we get

m²2/3=16

m²=16* 3/2

m²=24

m =2√6

Answer 2

The value of m is $m=-5\sqrt{2}$

Step-by-step explanation:

Given : If  $\frac{\sqrt2}{3}$  is a solution of equation $3x^2 + mx +2=0$.

To find : The value of m ?

Solution :

Equation $3x^2 + mx +2=0$.

The solution of equation means $x=\frac{\sqrt2}{3}$

Substitute in the equation,

$3(\frac{\sqrt2}{3})^2 + m(\frac{\sqrt2}{3}) +2=0$

$3(\frac{4}{9}) + m(\frac{\sqrt2}{3}) +2=0$

$\frac{4}{3}+ m(\frac{\sqrt2}{3}) +2=0$

$\frac{10}{3}+ m(\frac{\sqrt2}{3})=0$

$m(\frac{\sqrt2}{3})=-\frac{10}{3}$

$m=-\frac{10\times 3}{3\times \sqrt{2}}$

$m=-5\sqrt{2}$

Therefore, the value of m is $m=-5\sqrt{2}$

#Learn more

3x^2 + mx + 2 = 0 Find the value of m.

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