Quadratic Equations

Predict the signs of the roots just by looking at the equation sign. This helps you compare X and Y instantly without calculating values.

• ++ Equation: Roots will be (-, -).
• -+ Equation: Roots will be (+, +).
• +- Equation: Roots will be (+, -) (Larger root is Negative).
• -- Equation: Roots will be (+, -) (Larger root is Positive).

Find two numbers that multiply to $a \times c$ and add/subtract to $b$. Then Divide by 'a' and Change Variable Sign.

• Step 1: Find factors.
• Step 2: Change their signs.
• Step 3: Divide by coefficient $a$.

Systematically compare both X roots with both Y roots.

• Compare $x_1$ with $y_1, y_2$.
• Compare $x_2$ with $y_1, y_2$.
• If ALL comparisons say $>$, then $x > y$.
• If one says $>$ and another $<$, then CND.

Sometimes exams ask for $x$ and $y$ from linear sets like $2x + 3y = 12$. Use Co-efficient Elimination.

• Multiply equations to make one coeff equal.
• Subtract to find one variable.
• Substitute to find the other.