Question

For what value of k, is -2 a zero of the polynomial 3x²+4x+2k?​

Answer 1

x =-2

3x^2+4x+2k=0

3×-2^2+4×-2+2k=0

3×4-8+2k=0

12-8+2k=0

4 + 2k =0

2k = -4

k =-2

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Answer 2

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Q) For what value of k , is -2 a zero of the Polynomial 3x² + 4x + 2k ?

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☆ Given :–

• Polynomial : 3x² + 4x + 2k .
• -2 is a zero of this Polynomial .

☆ To Find :–

• The value of k

☆ Solution :–

We know that , a zero of a Polynomial when put in the place of the varible , makes the whole Polynomial equal to zero .

So ,

Put x = -2 in the given Equation and equate it with zero .

$\rm \mapsto \: 3 {x}^{2} + 4x + 2k = 0$

$\mapsto \rm \: 3 {( - 2)}^{2} + 4\times( - 2) + 2k = 0$

$\mapsto \rm \: 3 \times 4 + ( - 8) + 2k = 0$

$\mapsto \rm \: 12 - 8 + 2k = 0$

$\mapsto \rm \: 4 + 2k = 0$

$\mapsto \rm \: \cancel2k = - \cancel 4$

$\longrightarrow \underline{\boxed{ \sf{ \pink{k = - 2}}}}$

So ,

For k = -2 ,

-2 is a zero of the Polynomial .

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☆ Know More :–

• Zero of a Polynomial : It is that value of the variable , that makes the whole Polynomial = 0 .

• A zero of a Polynomial is also referred as the root of the Polynomial .

• In the case of Quadratic Polynomial , there are 2 zeroes / roots .

• To Find the zeroes/roots of a Quadratic Polynomial , we can use Middle term splitting or Quadratic Formula .