State whether k is the root of the given equation y2 – (k – 4)y – 4k = 0.

4. State whether k is the root of the given equation y² – (k – 4)y – 4k = 0.

Sol. y² – (k – 4)y – 4k = 0.

By putting y = k in L.H.S. we get

L.H.S. = (k)² – (k – 4)(k) – 4k

= k² – (k² – 4k) – 4k

= k² – k² + 4k – 4k

= 0

= R.H.S.

∴ L.H.S. = R.H.S.

Thus equation is satisfied.

So, k is the root of the given quadratic equation.