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.
