Class 10 Mathematics | Solving Quadratic Equations by Using the Formula

Activity 3

Method

Write the general quadratic equation \( ax^2 + bx + c = 0 \) in your copy.
Subtract \( c \) from both sides to get \( ax^2 + bx = -c \).
Divide both sides by \( a \) so that the coefficient of \( x^2 \) is 1.
Complete the square using \( \left(\frac{b}{2a}\right)^2 \), the square of half the coefficient of \( x \).
Write the left side as \( \left(x + \frac{b}{2a}\right)^2 \) and bring the right side to a single fraction.
Take the square root of both sides, keeping the sign \( \pm \).
Make \( x \) the subject and write down both roots.

Discussion

Why must \( a \neq 0 \) before dividing by \( a \)?
Why does the sign \( \pm \) appear when the square root is taken, and how many roots does it give?

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