Question

if one of the root of quadratic equation 2 X square + kx - 2 is equals to zero is minus 2 then find the value of k​

Answer 1

$\huge{\underline{\underline{\red{\mathfrak{Question :}}}}}$

if one of the root of quadratic equation 2 X square + kx - 2 is equals to zero is minus 2 then find the value of k .

$\huge{\underline{\underline{\red{\mathfrak{Answer :}}}}}$

Equation is 2x² + kx - 2 = 0

If one of the zeros is -2 then substitute value of x as -2 in the equation :

$\rightarrow {\sf{2(-2)^2 \: -2(k)\: - 2 \: = \: 0}}$

$\rightarrow {\sf{2(4) \: - 2k - 2 \: = \: 0}}$

$\rightarrow {\sf{8 \: -2k \: -2 \: = \: 0}}$

$\rightarrow {\sf{-2k \: + \: 6 \: = \: 0}}$

$\rightarrow {\sf{\cancel{-}2k \: = \: \cancel{-}6}}$

$\rightarrow {\sf{k \: = \: \dfrac{\cancel{6}}{\cancel{2}}}}$

$\LARGE \implies {\boxed{\boxed{\tt{k \: = \: 3}}}}$

Proof

For getting proof put value of x and if the equation get equal to zero. Hence the value of k will be verified.

Put Values

⇒2(-2)² + (3)(-2) -2 = 0

⇒2(4) -6 - 2 = 0

⇒8 - 6 - 2 = 0

⇒0 = 0

Hence Proved

Answer 2

The Value of k is 3.

Explaination :-

Given :-

Factor of Quadratic polynomial 2x² + kx -2 = 0 is -2.

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To Find :-

We have to solve Qiadratic polynomial 2x² + kx - 2

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Solution :-

As, It is given that the factor of polynomial is -2. So, put Value of x in the polynomial.

A.T.Q

2(-2)² + k(-2) - 2 = 0

2(4) - 2k - 2 = 0

6 - 2k = 0

6 = 2k

k = 6/2

k = 3

Hence, Value of k is 3.

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Verification :-

For, Verification put value of x in the quadratic polynomial and also put value of k and put it equal to the 0. If our L.H.S is equal to R.H.S then it is verified.

2(-2)² + 3(-2) -2 = 0

2(4) - 6 - 2 = 0

8 - 8 = 0

L.H.S = R.H.S

Hence Verified