1
Identify a = 2, b = -7, c = 3
3
Find two numbers whose product = 6 and sum = -7
These are -6 and -1 (since -6 × -1 = 6 and -6 + (-1) = -7)
4
Rewrite: 2x² - 6x - x + 3 = 0
5
Factor: 2x(x - 3) - 1(x - 3) = 0
7
Roots are x = 1/2 and x = 3
Worked Example 2:
Find the equation whose roots are 3 and -2.
1
Sum of roots = 3 + (-2) = 1
2
Product of roots = 3 × (-2) = -6
3
Using x² - (sum of roots)x + (product of roots) = 0
4
Required equation: x² - x - 6 = 0
Shortcut Trick #3 - Vieta's Relations:
Instead of finding individual roots, use sum and product formulas directly. This is especially useful when questions ask about expressions involving roots without finding the actual roots.
Common Trap - The #1 Mistake:
Students often forget to check if 'a' equals zero. If a = 0, the equation becomes linear (bx + c = 0), not quadratic. Always verify that the coefficient of x² is non-zero before applying quadratic methods. Another common error is sign mistakes while applying the quadratic formula, especially with the discriminant calculation