Solve the equation from p37: x² − 4x − 24 = 0 has which root pair? (Take the one valid for an age.)

x = 2 + 2√7. D = 16 + 96 = 112. x = 4 ± √1122 = 2 ± 2√7. The age must be positive, so x = 2 + 2√7.

Solve the equation from p37: $x^{2} - 4 x - 24 = 0$ has which root pair? (Take the one valid for an age.)

Class 10Quadratic EquationsAlgebra — Quadratics

D = 16 + 96 = 112. x = \frac{4 \pm 112}{2} = 2 \pm 27

. The age must be positive, so

x = 2 + 27

Answer: A)

x = 2 + 27

Rewrite

a x^{2} + b x + c

into the form

a (x - h)^{2} + k

.

**Steps for

x^{2} + b x + c = 0

**:
1. Take half the coefficient of

x : b /2

.
2. Square it:

(b /2)^{2}

.
3. Add and subtract this value to complete the perfect square.

Example:

x^{2} + 6 x + 5 = 0

.
→

(x^{2} + 6 x + 9) - 9 + 5 = 0

→

(x + 3)^{2} = 4

→

x + 3 =

±2 →

x = - 1

or −5.

Completing the square is how the quadratic formula is DERIVED. It's slower than factorisation but works ALWAYS (no clever guessing required).

Don't just memorise the answer — build a daily practice habit.