How do you find the value of the discriminant and determine the nature of the roots $x^2 + 9 = 6x$ ?

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Answer 1 · 2016-07-12T09:41:23

$Delta=0$

The given quadr. eqn. has two equal roots.

The discriminant $Delta$ of a Quadratic Eqn. $: ax^2+bx+c=0$ is given by,

$Delta=b^2-4ac$ .

The quadr. eqn. given to us is $:x^2+9=6x$
$=>x^2-6x+9=0.$

Therefore, $a=1, b=-6, c=9$
$rArr Delta=(-6)^2-4*1*9=36-36=0$

$rArr$ The given quadr. eqn. has two equal roots.

Answer 2 · 2016-07-12T14:23:09

double-root at x = 3

y = x^2 - 6x + 9 = (x - 3)^2
There is a double-root at x = 3. The parabola is tangent to x-axis
at x = 3. Vertex (3, 0)

How do you find the value of the discriminant and determine the nature of the roots x^2 + 9 = 6xx^2 + 9 = 6x?