Quadratic Equations
Quadratic Equations tests standard form, factorisation, the quadratic formula, discriminant and word problems. BSEB frequently asks for the nature of roots and for roots in exact or decimal form.
Core rules
Standard form ax²+bx+c=0, a≠0. Discriminant D=b²-4ac.
- D>0: two distinct real roots.
- D=0: two equal real roots.
- D<0: no real roots. Roots: x=(-b±√D)/(2a). Factorisation uses splitting the middle term. For a word problem, form the equation, solve, then reject values that do not fit the context.
Worked example
Solve 2x²-7x+3=0. Here a=2, b=-7, c=3. D=(-7)²-4(2)(3)=49-24=25. Roots = (7±5)/4. So x=12/4=3 or x=2/4=1/2. Check: 2(9)-21+3=0 and 2(1/4)-7/2+3=0.
Traps
D must be computed with b including its sign; (-7)²=49, not -49. The denominator is 2a, not a. If D<0, say “no real roots”, not “no roots” unless complex numbers are in scope. Do not cancel a variable that could be zero. In factorisation, the split numbers must multiply to ac and add to b. Always substitute both roots back or check the product.