Question

Determine the value of k for which the given value is a solution of the equation kx^2 – x – 6 = 0, x = 2.

Answer 1

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p(x) = kx²-x-6=0

g(x) = x= 2

p(x) = k(2)²-(2)-6

= 4k-2-6

= 4k-8

4k = 8

k = 8/4

k = 2

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Answer 2

AnsWer :

k = 2.

SolutioN :

☛ Condition :

• P( x ) = 2.

$\rule{80}2$

$\tt \dagger \: \: \: \: \: k {x}^{2} - x - 6 = 0.$

✎ Now, Putting the value x = 2.

$\tt : \implies k {(2)}^{2} - 2 - 6 = 0.$

$\tt : \implies 4 {k}^{2} - 8= 0.$

$\tt : \implies \cancel{4}{k}^{2} = \cancel8.$

$\tt : \implies {k}^{2} = 4.$

$\tt : \implies k= \sqrt{2}$

$\tt : \implies k= \pm2.$

✡ Therefore, the value of k is 2.

$\rule{200}3$

VerificatioN :

→ 2x² - x - 6 = 0.

→ 2x² - 4x + 3x - 6 = 0.

→ 2x( x - 2 ) + 3( x - 2 ) = 0.

→ ( 2x + 3 )( x - 2 ) = 0.

✎ Either,

→ x - 2 = 0.

→ x = 2.

✎ Or,

→ 2x + 3 = 0.

→ x = - 3/2.

Hence Verify.