Question

tell me the shortcuts for quadratic equations

Answer 1

Short Trick Method :
In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer

1) if x > y
2) if x < y
3) if x ≥ y
4) if x ≤ y
5) if x = y or relation cannot be established between 'x' and 'y'.

I. 2x² - 11x +12=0 , II. 2y²-17y+36=0

Equation I :- 2x²-11x+12=0

1. multiple X² coefficient and constant term = 12 × 2= 24

2. Split X coefficient in order to get its sum is -11 and its multiplication is 24. It's -8 and -3 .

3.Now change signs -8 = 8 and -3 = 3.

4. Divide these numbers with X² coefficient 8/2 = 4 and 3/2 = 1.5

5. X1 = 4 ; X2 = 1.5

Equation II :- 2y²-17y+36=0

It's also similar to equation I

1. multiple Y² coefficient and constant term = 2×36 =72

2. Split X coefficient in order to get its sum is -17 and its multiplication is 72. It's -9 and -8 .

3.Now change signs -9 = 9 and -8 = 8.

4. Divide these numbers with X² coefficient 9/2 = 4.5 and 8/2 = 4 .

5. Y1 = 4.5 , Y2= 4

Compare X and Y values

Case 1 : X1(4)< Y1(4.5)
Case 2 : X1(4) = Y2(4)
Case 3 : X2(1.5) < Y1(4.5)
Case 4 : X2(1.5) < Y2 (4)

From above 4 Cases we can easily find out relation between X and Y

Answer : X ≤ Y



hope it helps u