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#### 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.

Example :

X2 – 5X + 6 =0
Y2 +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 :
X2 -3X – 2X +6 =0

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

Y2 -10Y +24 = 0

• Y2 -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 ax2 + bx +c =0 where a,b &c  £ R  and a ≠ 0 has two roots namely.