Question

Use the discriminant to determine all values of k that would result in the equation x^2-kx+4=0 having equal roots

Answer 1

Equal roots mean there is only one root for this quadratic equation.

Answer 2

Discriminant = \(b^2 - 4ac\).

Answer 3

That means that the discriminant is zero.

Answer 4

As @bloopman mentioned, \[D=b^2-4ac=0\].

Answer 5

Now, a=1, b=-k and c=4.

Answer 6

So, \[(-k)^2-(4)(4)(1)=k^2-16=0\]

Answer 7

k can be 4 or -4

Answer 8

Use the discriminant to determine all values of k that would result in the equation x^2-kx+4=0 having equal roots

having equal roots implies that the discriminant is \(0\):$$b^2-4ac=0\\k^2-4(1)(4)=0\\k^2-16=0\\(k+4)(k-4)=0$$ergo \(k=\pm4\)

Answer 9

hmmm i would say
\[x^2-kx+4\] is a perfect square if you take half of \(4\) and square the result