If Zeba were younger by \(5\) years than what she really is, then the square of her age (in years) would have been \(11\) more than five times her actual age. What is her age now?
14 years
Step 1: Assume her present age.
Let Zeba's present age be \(x\) years.
Step 2: Write the condition given in the question.
If Zeba were 5 years younger, her age would be \(x - 5\).
The square of this age is \((x - 5)^2\).
This square is equal to "five times her actual age + 11".
So, the equation is: \((x - 5)^2 = 5x + 11\).
Step 3: Expand the square.
\((x - 5)^2 = x^2 - 10x + 25\).
So the equation becomes: \(x^2 - 10x + 25 = 5x + 11\).
Step 4: Bring all terms to one side.
\(x^2 - 10x + 25 - 5x - 11 = 0\).
\(x^2 - 15x + 14 = 0\).
Step 5: Solve the quadratic equation.
Factorise: \(x^2 - 15x + 14 = (x - 14)(x - 1) = 0\).
So, \(x = 14\) or \(x = 1\).
Step 6: Check which answer is possible.
If \(x = 1\), then her age 5 years ago would be negative, which is not possible.
So, the only valid answer is \(x = 14\).
Final Answer: Zeba’s age is 14 years.