Question

Given −7 is one of the roots of the quadratic equation

Answer 1

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Taking square root on the both sides of equation (x + k)² = 16 we get,

$\implies\rm{( {x + k)}^{2} } = 16$

$\implies\rm{x + k = ± 4}$

Making two conditions for ± 4 i.e

1) x + k = 4

$\implies\rm{ - 7 + k = 4}$

$\implies\rm{k = 4 + 7}$

$\implies\rm{k = 11}$

2) x + k = -4

$\implies\rm{ - 7 + k = - 4}$

$\implies\rm{k = - 4 + 7}$

$\implies\rm{k = 3}$

• Thus the values of k can be either 11 or 3.

Answer 2

Answer:

  k = {3, 11}

Step-by-step explanation:

Taking the square root of the given equation, we find ...

  x +k = ±4

For x = -7, this is ...

  -7 +k = ±4

  k = 7 ±4 = {3, 11}

Possible values of k are 3 and 11.