Question

Please please please please help!!!
what are the linear factors of the quadratic equation x^2+kx+1

Answer 1

The linear factor is "(x + 1) or (x - 1)".

Step-by-step explanation:

The given quadratic equation,

$x^{2}$ + kx + 1 = 0     ......(1)

Here, a = 1, b = k and c = 1

∴ D = $b^{2}$ - 4ac

= $k^{2}$ - 4 × 1 × 1

= $k^{2}$ - 4

= (k + 2)(k - 2) ≥0

= (k + 2)(k - 2) = 0

∴ k = 2 or -2

Put k = 2 in equation(1), we get

$x^{2}$ + 2x + 1 = 0  

⇒ $(x + 1)^{2}$ = 0

⇒ x + 1 = 0

Put k = - 2 in equation(1), we get

$x^{2}$ - 2x + 1 = 0  

⇒ $(x - 1)^{2}$ = 0

⇒ x - 1 = 0

Hence, the linear factor is "(x + 1) or (x - 1)".

Answer 2

hope it may help u very much