661d43a6d705430018fb4907_##_Algebra 03 Class Notes MBA Elite 2024.pdf

Quadratic equation nites

1. TARGET CAT 2024
QUANT - II
Quadratic Equations - 1
Lecture No.- 03
By- VINIT KAKRIYA SIR
MBA Elite 2024

2. Recap of Previous Lecture :

3. 1)Number of Integral Solutions in Linear Equation
2)Concepts involved in Quadratic Equation
3)Problems for Practice & CAT PYQs
to be covered

4. Number of Integral Solutions in Linear Equation :

5. Number of Integral Solutions in Linear Equation :

6. QUESTION- 1
#Q. If x and y are non negative integers. Find the number of solutions of equation.
3x + 5y = 48
4A
3B
1C
2D

7. QUESTION- 2
#Q. If x and y are positive integers. Find the number of solutions of equation.
3x + 11y = 330
10A
9B
11C
Cannot be determinedD

8. QUESTION- 3
#Q. If x and y are positive integers. Find the number of solutions of equation.
2x + 5y = 99
10A
9B
11C
None of theseD

9. QUESTION- 4
#Q. The number of pairs of integers(x, y) satisfying x ≥ y ≥ -20 and
2x + 5y = 99 is [CAT 2020: Slot 2]

10. QUESTION- 5
#Q. If 2�+3�+4�=9, find the value of ‘���’ given that ‘a’ ,′�′ �??????� ′�′ are
positive integers.

2A
1B
0C
-1D

11. QUESTION- 6
#Q. If 2�+3�+4�=16, find the value of ‘�−�−�’ given that ‘a’ ,′�′ �??????� ′�′ are
distinct positive integers.
2A
1B
0C
-1D

12. Quadratic Equations

13. Concepts involved in Quadratic Equation :

14. Concepts involved in Quadratic Equation :

15. Concepts involved in Quadratic Equation :

16. Concepts involved in Quadratic Equation :

17. Concepts involved in Quadratic Equation :

18. Concepts involved in Quadratic Equation :

19. Concepts involved in Quadratic Equation :
Points to Remember :
1.Quadratic Equations are represented as
a�
2
+ bx + c = 0, where a ≠ 0
2. Discriminant (D) = �
2
- 4ac
* If D > 0 ---------- Roots are Real & Unequal
* If D = 0 ---------- Roots are Real & Equal
* If D < 0 --------- Roots are Imaginary (Complex Roots or No Real Roots)

3.If one of the roots of Quadratic Equation is (x +&#3627408486;), then other root can be represented as (x −&#3627408486;)
& vice versa.
4. If &#3627409148; & &#3627409149; are the roots of quadratic equation a&#3627408485;
2
+ bx + c = 0, then
Sum of Roots (&#3627409148; + &#3627409149;) =
− &#3627408463;
&#3627408462;
& Product of Roots (&#3627409148;&#3627409149;) =
&#3627408464;
&#3627408462;
5. If &#3627409148; & &#3627409149; are the roots of quadratic equation, then equation can be represented as &#3627408485;
2
- (&#3627409148;+&#3627409149;)x + &#3627409148;&#3627409149; = 0

20. QUESTION- 1
#Q. If the product of roots of the equation x
2
– 3(2p + 4)x + p
2
+ 18p + 81 = 0 is
unity, then p can take the value as
3, -6A
10, -8B
-10, -8C
-10, -6D

21. QUESTION- 2
#Q. For some real numbers ‘a’ and ‘b’. The system of equations &#3627408485; + &#3627408486; =4 &#3627408462;??????&#3627408465;
(&#3627408462;+5)&#3627408485; +&#3627408463;
2
−15&#3627408486; =8&#3627408463; has infinitely many solutions for x & y. Then, the
maximum possible value of ‘ab’ is [CAT 2023 : Slot 3]
15A
33B
55C
25D

22. QUESTION- 3
#Q. If  &  be the roots of the equation 2&#3627408485;
2
- 4x - 3 = 0 the value of 
2
+ 
2
is

5A
7B
3C
-4D

23. QUESTION- 4
#Q. If one root of 5&#3627408485;
2
+ 13x + p = 0 be reciprocal of the other then the value of p
is
-5A
5B
1/5C
-1/5D

24. QUESTION- 5
#Q. If the root of the equation &#3627408485;
2
- 8x + m = 0 exceeds the other by 4 then the
value of m is
10A
11B
9C
12D

25. QUESTION- 6
#Q. A root of equation ax
2
+ bx + c = 0 is 5 + 33. What is the value of
&#3627408462;
2
+&#3627408463;
2
+&#3627408464;
2
&#3627408462;+&#3627408463;+&#3627408464;
?
35/3A
-105/11B
-105/13C
37/3D

26. QUESTION- 7
#Q. If (3 + 22) is a root of the equation a&#3627408485;
2
+ bx + c = 0, and (4 + 23) is a root of
the equation a&#3627408486;
2
+ my + n = 0, where, a, b, c, m and n are integers, then the value of
(
&#3627408463;
&#3627408474;
+
&#3627408464; −2&#3627408463;
&#3627408475;
) is [CAT 2022 : Slot 3]
0A
1B
3C
4D

27. 2 Mins Summary
1)Number of Integral Solutions in Linear Equation
2)Concepts involved in Quadratic Equation
3)Problems for Practice & CAT PYQs

28. Thank
You