QUADRATIC EQUATIONS
- A polynomial of degree 2 is called Quadratic Equation.
- A general form of quadratic equation is ax2 + bx + c = 0
- Two quadratic equations are given in the questions. We have to find out the values of the variables
and compare them. Based on the relation, conclusions have to be made.
Directions (Q. 1-5) : In each of the questions below, two
equations are provided. On the basis of these you have to
find out the relation between x and y.
Give answer
(1) If x = y
(2) If x > y
(3) If x < y
(4) If x ≥ y
(5) If x ≤ y
1. x2 + 8x + 15 = 0; y2 + 11y + 30 = 0(4)
- x2 + 7x = 30; y2 – 64 = 0(3)
- 3x + y – 1 = 0; 8x + 12y – 5 = 0(1)
- x2 – 5x + 66 = 0; y2 – 10y = 11(5)
- 2x2 + 3x = 2; 2y2 + 11y = –15(2)
Directions (Q. 6-10) : In each of the questions below, two
equations are provided. On the basis of these you have to
find out the relation between x and y.
Give answer
(1) If x = y
(2) If x > y
(3) If x < y
(4) If x ≥ y
(5) If x ≤ y
- x2 – x – 12 = 0; y2 – 7y + 12 = 0(5)
- x2 – 2x – 35 = 0; y2 – 6y + 27 = 0(3)
- x2 – 10x + 16 = 0; y2 + y – 30 = 0(2)
- 2x2 + 3x = 2; 2y2 + 11y = –15(2)
- 3x + y – 1 = 0; 8x + 12y – 5 = 0(1)
EXPLANATIONS
1. On solving, x values are –5 and –3, y values are –5 and –6.
∴ x ≥ y
2. On solving, x values are –10 and 3, y values are 8 and –8
∴ x < y
3. On solving, both x and y values are 1/4 and 1/4
∴ x = y
4. On solving, x values are 11 and –6, y values are 11 and –1
∴ x ≤ y
5. On solving, x values are 1/2 and –2, y values are –3 and 5/2
∴ x > y
6. On solving we get, x values as 4 and –3, y values as 4 and 3
∴ x ≤ y
7. On solving we get, x values as 7 and –5, y values as 9 and –3
∴ x < y
8. On solving we get, x values as 8 and 2, y values are 5 and –6
∴ x > y
9. On solving, x values are 1/2 and –2 , y values are –3 and – 5/2
∴ x > y
10. On solving, both x and y values are 1/4 and 1/4
∴ x = y.