Question

If one of the roots of the quadratice quation x2+kx-12=0is4,what is the value of k?

Answer 1

Given Equation:

`\huge \purple {\rm { {x}^(2) + kx - 12 = 0}}`

Value:

`\huge \purple {\rm {x = 4}}`

To Find:

`\huge \purple {\rm {The \: value \: of \: k.}}`

Solution:

`\huge \purple {\rm { {(4)}^(2) + k(4) - 12 = 0}}`

`\huge \purple {\rm {or, \: 16 + 4 k - 12 = 0}}`

`\huge \purple {\rm {or, \: 4k = - 4}}`

`\huge \purple {\rm {or, \: k = ( - 4)/(4) = - 1}}`

Answer:

`\huge \purple {\sf {The \: value \: of \: k \: is \: -1}}`

Answer 2

k = - 1

Explanation:

Given that x = 4 is a root then, substitute x = 4 into the equation.

4² + 4k - 12 = 0

16 + 4k - 12 = 0, that is

4k + 4 = 0 ( subtract 4 from both sides )

4k = - 4 ( divide both sides by 4 )

k = - 1