Set-2 Quadratic Equations (Inequalities) For SBI PO and SBI Clerk 2019 | Must Go Through These Questions

• If p > q
• If p < q
• If p ≥ q
• If p ≤ q
• If p = q (or) no relation can be established between p and q.

10.

• Directions:1-5) In the given question two equations are given. You have to Solve both the equations and given answer.

  1. Question

  I.x² +11x +18 = 0
  II.y² +16y+ 48 = 0

  • If x > y
  • If x <y
  • If x ≥ y
  • If x ≤ y
  • If x= y or relationship between x & y cannot be established.
  Ans:5
  I)x² +11x +18 = 0
  x² +2x+9x+18=0
  x(x+2)+9(x+2)=0
  (x+2) (x+9)=0
  x=-2,-9y² +16 y+ 48 = 0
  y²+4y+12y+48=0
  y(y+4) + 12(y+4)=0
  (y+4)(y+12)=0
  y=-4,-12
  So relationship between x and y cannot be established

• 2. Question

  I.3x² +10x +7 = 0
  II.3y² +4y+ 1 = 0

  • If x > y
  • If x <y
  • If x ≥ y
  • If x ≤ y
  • If x= y or relationship between x & y cannot be established.
  Ans:4
  I.3x² +10x +7 = 0
  3x² +3x+7x+7=0
  3x(x+1) + 7(x+1)=0
  (x+1) (3x+7)=0
  x=-1,-7/3II.3y² +4y+ 1 = 0
  3y² + 3y+y+1=0
  3y(y+1) + 1(y+1) =0
  (y+1) (3y+1)=0
  y=-1,-1/3
  So x ≤ y

• 3. Question

  I.5x² -7x +2 = 0
  II.2y² -7y+ 3 = 0

  • If x > y
  • If x <y
  • If x ≥ y
  • If x ≤ y
  • If x= y or relationship between x & y cannot be established.
    Ans:5
  I.5x² -7x +2 = 0
  5x²-5x-2x+2=0
  5x(x-1) -2(x-1)=0
  (x-1) (5x-2)=0
  x=1,2/5II.2y² -7 y+ 3 = 0
  2y²-6y-y+3=0
  2y(y-3) -1(y-3)=0
  (y-3) (2y-1)=0
  y=3,1/2
  Relationship between x and y cannot be established

• 4. Question

  I.2x² -3x +1 = 0
  II.y²-8 y+ 15 = 0

  • If x > y
  • If x <y
  • If x ≥ y
  • If x ≤ y
  • If x= y or relationship between x & y cannot be established.
  Ans:2
  I.2x² -3x +1 = 0
  2x² -2x-x +1=0
  2x(x-1)-1(x-1)=0
  (x-1) (2x-1)=0
  x=1,1/2II.y²-8 y+ 15 = 0
  y²-3y-5y+15=0
  y(y-3)-5(y-3)=0
  (y-3)(y-5)=0
  y=3,5
  So x <y

• 5. Question

  I)x = (-4)²
  II)y²=256

  • If x > y
  • If x <y
  • If x ≥ y
  • If x ≤ y
  • If x= y or relationship between x & y cannot be established.
  Ans:3
  I)x = (-4)²x=16

  II)y²=256

  y=16 and -16

  Hence x ≥ y

  Directions:6-10):Two equations (I) and (II) are given in each question. On the basis of these questions, you have to decide the relation between p and q and give answer

  6. Question

  1. 5p²– 87p + 378 = 0
  2. 3q²– 49q + 200 = 0

  • If p > q
  • If p < q
  • If p ≥ q
  • If p ≤ q
  • If p = q (or) no relation can be established between p and q.
    Ans:1
  I.5p² – 45p – 42p + 378 = 05p (p – 9) – 42(p- 9) = 0

  (5p – 42)(p -9) = 0

  p = 9, 42/5 = 9, 8.4

  II.3q² – 24q – 25q + 200=0

  3q (q – 8) -25(q – 8) = 0

  (q – 8)(3q-25)=0

  q = 8, 25/3 = 8, 8.33

  Hence, p>q

• 7. Question

  1. 10p²– p – 24 = 0
  2. q²– 2q = 0

  • If p > q
  • If p < q
  • If p ≥ q
  • If p ≤ q
  • If p = q (or) no relation can be established between p and q.
  Ans:5
  I.10p² +15p – 16p – 24 = 05p(2p + 3) – 8(2p+ 3)=0

  (2p + 3)(5p – 8) = 0

  p = -3/2, 8/5 = -1.5, 1.6

  II.q²– 2q = 0

  q(q -2) = 0

  q = 0, 2

  (i.e.) no relationship exists between p and q.

• 8. Question

  1. p²– 5p + 6 = 0
  2. 2q²– 15q + 27 = 0

  • If p > q
  • If p < q
  • If p ≥ q
  • If p ≤ q
  • If p = q (or) no relation can be established between p and q.
  Ans:4
  p² – 2p – 3p + 6 =0p(p -2) – 3(p -2) = 0

  (p -2) (p -3) = 0

  p =2, 3

  2q²  – 6q – 9q + 27 = 0

  2q(q – 3)-9(q -3) = 0

  (q- 3) (2q -9) = 0

  q = 3, 9/2 = 3, 4.5

  Hence, p ≤ q

• 9. Question

  1. 3p + 2q = 301
  2. 7p – 5q = 74

  • If p > q
  • If p < q
  • If p ≥ q
  • If p ≤ q
  • If p = q (or) no relation can be established between p and q.
    Ans:2
  I.eqn (I) × 5 + eqn (II) × 2[15p + 10q = 1505] + [14p – 10q = 148] = 29p = 1653

  p = (1653/29) = 57

  And q = 65

  Hence, p< q

• 10. Question

  1. 14p²– 37p + 24 = 0
  2. 28q²– 53q + 24 = 0

  • If p > q
  • If p < q
  • If p ≥ q
  • If p ≤ q
  • If p = q (or) no relation can be established between p and q.
  Ans:3
  14p² – 37p + 24 = 014p² – 21p- 16p + 24 = 0

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

  (2p – 3)(7p – 8) = 0

  p = (3/2), (8/7)

  II.28q² – 53q + 24 = 0

  28q²  -21q – 32q + 24 =0

  7q(4q – 3) -8(4q – 3) = 0

  (7q – 8) (4q – 3) = 0

  q = 8/7, 3/4

  p ≥ q