Question

for what value of k is -2 a root of the equation 3 X square + 4 x + 2 K is equal to zero​

Answer 1

$\large\bf\underline \orange{Given:-}$

• p(x) = 3x² + 4x +2k

$\large\bf\underline \orange{To \: find:-}$

• For what value of k is -2 a root of the equation 3 X square + 4 x + 2 K is equal to zero.

$\huge\bf\underline \green{Solution:-}$

Let -2 be a root of the given equation.

• x = -2

putting value of x in the given equation.

$:\implies\rm\:3 {x}^{2} + 4x + 2k = 0 \\ \\ :\implies\rm\:3 \times ( - 2 {)}^{2} + 4 \times ( - 2) + 2k = 0 \\ \\ :\implies\rm\:3 \times 4 - 8 + 2k = 0 \\ \\ :\implies\rm\:12 - 8 + 2k \\ \\ :\implies\rm\:4 + 2k = 0 \\ \\ :\implies\rm\:2k = - 4 \\ \\ :\implies\rm\:k = \cancel\frac{ - 4}{2} \\ \\ :\implies\bf\:k = - 2$

If k = -2 then the quadratic equation 3 X square + 4 x + 2 K is equal to zero.

$\large \bf \underline{Verification} : -$

$: \implies \rm \: 3 {x}^{2} + 4x + 2k \\ \\ : \implies \rm \: 3 {( - 2)}^{2} + 4( - 2) + 2( - 2) \\ \\ : \implies \rm \: 12 - 8 - 4 \\ \\ : \implies \rm \: 12 - 12 \\ \\ : \implies \rm \: 0$

$\rm \: hence \bf \underline{ \: Verified \: \: }$

Answer 2

✯✯ QUESTION ✯✯

For what value of k is -2 a root of the equation ${3x}^{2} + 4x + 2K = 0$

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✰✰ ANSWER ✰✰

$\longmapsto\tt{{3x}^{2} + 4x + 2K = 0}$

➙Putting x = -2 : -

$\longmapsto\tt{{3(-2)}^{2}+4(-2)+2k=0}$

$\longmapsto\tt{3(4)-8+2k=0}$

$\longmapsto\tt{12-8+2k=0}$

$\longmapsto\tt{12-8=-2k}$

$\longmapsto\tt{4=-2k}$

$\longmapsto\tt{k=\cancel\dfrac{4}{-2}}$

$\red\longmapsto\:\large\underline{\boxed{\bf\green{k}\orange{=}\purple{-2}}}$

➜So , The value of k is -2 ..

_______________________

☛VERIFICATION : -

➙Putting k = -2 : -

$\longmapsto\tt{{3x}^{2} + 4x + 2K = 0}$

$\longmapsto\tt{{3(-2)}^{2}+4(-2)+2(-2)=0}$

$\longmapsto\tt{3(4)-8-4=0}$

$\longmapsto\tt{12-8-4=0}$

$\longmapsto\tt{4-4=0}$

$\purple\longmapsto\:\large\underline{\boxed{\bf\blue{0}\green{=}\red{0}}}$

✺ HENCE VERIFIED ✺