Set-21 Quadratic Equations (Inequalities) For SBI PO and SBI Clerk 2019 | Must Go Through These Questions

• x> y
• x< y
• x ≤ y
• x ≥ y
• x =y Or cannot be determined

10.
i) 5x²+36√3x+192=0
ii) 2y²+9√3y+27=0

Check your Answers below:

• Directions:1-5) In the following questions, two equations I and II are given. You have to solve both the equations.

  Give Answer

  1. Question

  I. 15a² – 10a – 5 = 0;
  II. 20b² + 18b + 4 = 0

  • If a > b
  • If a ≥ b
  • If a < b
  • If a ≤ b
  • If a = b or the relationship cannot be established
  Ans:5
  15 a² + 15a – 5a –  5 = 0

  15a (a + 1) – 5 (a + 1) = 0

  (15a – 5) (a + 1) = 0

  a = 1/3, -1

  20b² + 10b + 8b + 4 = 0

  10b (2b +1) + 4 (2b + 1) = 0

  (10b + 4) (2b + 1) = 0

  b = -2/5,    -1/2

  Hence there is no relation.

• 2. Question

  I. 26a² – 88 = 16;
  II. 3√b/8 – √b/4 = 1/√b

  • If a > b
  • If a ≥ b
  • If a < b
  • If a ≤ b
  • If a = b or the relationship cannot be established
  Ans:3
  26a² = 16 + 88 = 104

  a² = 104/26 = 4

  a = ±2

  3√b/8 – 2√b/8 = 1/√b

  √b/8 = 1/√b

  b = 8

  a < b.

• 3. Question

  I. 2a + 3b = 20;
  II. 4a + 2b = 24

  • If a > b
  • If a ≥ b
  • If a < b
  • If a ≤ b
  • If a = b or the relationship cannot be established
  Ans:5
  4a + 6b = 40 —-I

  4a + 2b = 24 —-II

  Solve I and II we get

  4b = 16

  b = 4

  Apply the b = 4 in eqn I

  a = 4

  a= b.

• 4. Question

  I. 10a² + 9a -7 = 0;
  II. 12b + 84 = 12²

  • If a > b
  • If a ≥ b
  • If a < b
  • If a ≤ b
  • If a = b or the relationship cannot be established
  Ans:3
  10a² + 14a – 5a – 7 = 0

  2a (5a + 7) – 1 (5a + 7) = 0

  (2a – 1) (5a + 7) = 0

  a = 1/2, -7/5

  12b = 144 – 84 = 60

  b = 60/12 = 5

  a < b.

• 5. Question

  I. a² = 196;
  II. b² + 11b + 24 = 0

  • If a > b
  • If a ≥ b
  • If a < b
  • If a ≤ b
  • If a = b or the relationship cannot be established
  Ans:5
  a = ±14

  b2 + 8b + 3b + 24 = 0

  b (b + 8) + 3 (b + 8) = 0

  (b + 3) (b + 8) = 0

  b = -3, -8

  Hence there is no relation.

  Directions:6-10) In each of the following questions, two equations (i) and (ii) are given. You have to solve them and find the correct option.

  6. Question

  i) 2x²+11x+12=0
  ii) x²+2x-35=0

  • x> y
  • x< y
  • x ≤ y
  • x ≥ y
  • x =y Or cannot be determined
  Ans:5
  a) 2x²+11x+12=0

  2x²+8x+3x+12=0

  (x+4)(2x+3)=0

  x= -4 and -3/2

  b) x²+2x-35=0

  x²+7x-5x-35=0

  (x+7)(x-5)=0

  x=-7 or 5

  Hence the relationship cannot be determined

• 7. Question

  i) x²-20x+99=0
  ii) 2y²-15y+28=0

  • x> y
  • x< y
  • x ≤ y
  • x ≥ y
  • x =y Or cannot be determined
  Ans:1
  a) x²-20x+99=0

  x²-9x-11x+99=0

  (x-9)(x-11)=0

  x=9 and 11

  b) 2y²-15y+28=0

  2y²-8y-7y+28=0

  (y-4)(2y-7)=0

  y= 7/2 and 4

  Thus x>y

• 8. Question

  i) 2x+5y-√2601=0
  ii) 7x+3y-77=0

  • x> y
  • x< y
  • x ≤ y
  • x ≥ y
  • x =y Or cannot be determined
  Ans:1
  After solving above equations we have x= 8 and y=7

  Hence x>y

• 9. Question

  i) x²+19y+90=0
  ii) 14y²-37y+24=0

  • x> y
  • x< y
  • x ≤ y
  • x ≥ y
  • x =y Or cannot be determined
  Ans:2
  a) x²+19y+90=0

  x²+9y +10y+90=0

  (x+9)(x+10)=0

  x= -9 and -10

  b) 14y²-37y+24=0

  14y²-21y-16y+24=0

  7y(2y-3)-8(2y-3)=0

  y= 3/2 or 8/7

  Hence x<y

• 10. Question

  i) 5x²+36√3x+192=0
  ii) 2y²+9√3y+27=0

  • x> y
  • x< y
  • x ≤ y
  • x ≥ y
  • x =y Or cannot be determined
  Ans:2
  a)5x²+36√3x+192=0

  5x²+20√3x+16√3x+192=0

  (5x+16√3)(x+4√3)=0

  x=-4√3 or -16√3/5

  b) 2y²+9√3y+27=0

  2y²+6√3y+3√3y +27=0

  (2y+3√3)(y+3√3)=0

  y= -3√3 or -3√3/2

  Thus x<y