Any form of the equation having second-degree polynomial in one variable is called quadratic equation. Typically in GMAT you have to deal with the equation form of y = ax2 + bx + c formula related to the quadratic equations that you need to mug up is
- Root of the the equation ax2 + bx + c = 0 is
- Determinant D is calculated as
If D=0, equation will have real and equal root
If D>0, equation will have real roots
If D<0, equation will have imaginary roots
Let’s look at some problems
- The sum of a number and its reciprocal is 10/3. Find the number.
Let the number be x.therefore x +1/x=10/3
Arranging the equation we get,
3x2 –10x + 3 = 0
(3x-1)(x-3) = 0
Therefore, x = 3, ⅓
- If x2 + bx + 72 = 0 has integral roots, find the number of values b can attain.
72 can be written as 2 x 2 x 2 x 3 x 3. Hence the number of positive pairs whose product is 72 is (3+1)(2+1)/2= 6.
Similarly, the number of negative pairs are 6. Hence 12 is the answer.