**Quadratic Equations Shortcut Tricks:**

#### Quadratic equations are also one of the scoring parts in aptitude section of bank exams. If you follow this logic/trick for solving these equations to find out the root values you can solve it in seconds of time.

- A quadratic equation has two roots.
- Solving a quadratic equation means finding its root values.
- Generally, the quadratic equation can be solved in two methods traditionally 1) factor Method 2)Formula. But the trick I have explained here different and time-saving technique(shortcut method).

Observe the below example and solve this example using all the above methods and decide yourself which one is better to move further.

### Quadratic Equations for PRACTICE With Shortcuts and Explaination

Example :

X^{2} – 5X + 6 =0

Y^{2} +24 = 10y . Find the relation between X and Y?

(1) X > Y (2) X < Y (3) X = Y (4) X ≤ Y (5) X ≥ Y.

Sol: (1) Factor Method :

**X ^{2} -3X – 2X +6 =0**

**X(X-3) – 2(X – 3) =0****(X-3)(X-2) =0****X=3, X=2**

**Y ^{2} -10Y +24 = 0**

**Y**^{2}-6Y -4Y +24 =0**Y(Y-6) -4(Y-6) =0****(Y-6)(Y-4) =0****Y=6, Y =4**

**Therefore, X < Y.**

Formula Method : The quadratic equation **ax ^{2} + bx +c =0 where a,b &c £ R and a ≠ 0 has two roots namely.**