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Quadratic Equations - Inequalities

  • 1) Quadratic Equation: 3x² - 7x + 8 = 0 (a) Find the Discriminant, (b)Real or Not Real Roots, (c) Equal (one) or Unequal Roots, (d) Rational or Irrational Roots?

  •   (a) -23 (b)Not Real (c)Unequal (d)None of these
  •   (a)7 (b) Real (c)None (d)None
  •   (a) -23 (b)Real (c)Equal (d)Rational
  •   (a)-47 (b) Not Real (c)None of these (d)None

  • 2) Quadratic Equation 4x² + 12x + 9 = 0 Find the (a)Discriminant, (b)Real or Not Real Roots, (c)Equal (one) or Unequal Roots, (d)Rational or Irrational Roots?

  •   (a)5 (b)Real (c)Equal Roots (d)Rational Roots
  •   (a)0 (b)Real (c)Equal Roots (d)Rational Roots
  •   (a)1 (b)Not Real (c)Equal Roots (d)Rational Roots
  •   (a)0 (b)Real (c)Equal Roots (d)Rational Roots

  • 3) Quadratic Equation 16x² + 8x +1 = 0 Find the (a) Discriminant, (b) Real or Not Real Roots, (c) Equal (one) or Unequal Roots, (d) Rational or Irrational Roots?

  •   (a)1 (b)Not Real (c)Equal (d)Rational Roots
  •   (a)0 (b)Real (c)Not Equal (d)Irrational Roots
  •   (a)5 (b)Not Real (c)Equal (d)Rational Roots
  •   (a)0 (b)Real (c)Equal (d)Rational Roots

  • 4) Quadratic Equation x² - 8x + 16 = 0 Find the (a) Discriminant, (b) Real or Not Real Roots, (c) Equal (one) or Unequal Roots, (d) Rational or Irrational Roots?

  •   (a)3 (b) Not Real (c)Equal (d)Rational Roots
  •   (a)2 (b)Real (c)Un Equal (d)Rational Roots
  •   (a)3 (b)Not Real (c)Equal (d)Rational Roots
  •   (a)0 (b)Real (c)Equal Roots (d)Rational Roots

  • 5) Quadratic Equation -x² + 4x + 5 = 0 Find the (a) Discriminant, (b) Real or Not Real Roots, (c) Equal (one) or Unequal Roots, (d) Rational or Irrational Roots?

  •   (a)0 (b)Not Real (c)Equal Roots (d)Rational Roots
  •   (a)0 (b)Real Roots (c)Un Equal Roots (d)Irrational Roots
  •   (a)1 (b)Not Real (c)Equal Roots (d)Irrational Roots
  •   (a)-4 (b)Not Real (c)None (d)None

  • 6) Quadratic Equation -2x² -9x - 5 = 0 Find the (a) Discriminant, (b) Real or Not Real Roots, (c) Equal (one) or Unequal Roots, (d) Rational or Irrational Roots?

  •   (a)41 (b)Not Real (c)None (d)None
  •   (a)-1 (b)Real (c)Not Equal (d)Irrational Roots
  •   (a)0 (b)Not Real (c)Equal (d)Rational Roots
  •   (a)-3 (b)Not Real (c)None (d)Rational Roots

  • 7) Quadratic Equation 2x² + 7x + 3 = 0 Find the (a) Discriminant, (b) Real or Not Real Roots, (c) Equal (one) or Unequal Roots, (d) Rational or Irrational Roots?

  •   (a)Discriminant = 17 (b)Real (c)Equal Roots (d)Irrational Roots
  •   (a)25 (b)Real (c)Not Equal Roots (d)Rational Roots
  •   (a)5 (b)Not Real (c)Equal Roots (d)Rational Roots
  •   (a)15 (b)Real (c)Not Equal Roots (d)Rational Roots

  • 8) Quadratic Equation 3x² + 6x + 1 = 0 Find the (a) Discriminant, (b) Real or Not Real Roots, (c) Equal (one) or Unequal Roots, (d) Rational or Irrational Roots?

  •   (a)4 (b)Real (c)Not Equal Roots (d)Irrational Roots
  •   (a)14 (b)Not Real (c)Equal Roots (d)Rational roots
  •   (a)-25 (b)Not Real Roots (c)Not Equal Roots (d)Irrational Roots
  •   (a)24 (b)Real (c)Not Equal Roots (d)Rational roots

  • 9) Quadratic Functions 4x² + 7x -2 = 0 Find the (a) Discriminant, (b) Real or Not Real Roots, (c) Equal (one) or Unequal Roots, (d) Rational or Irrational Roots?

  •   (a)87 (b)Not Real (c)Not Equal Roots (d)Rational Roots
  •   (a)85 (b)Real (c)Not Equal Roots (d)Rational Roots
  •   (a)51 (b)Real (c)Equal Roots (d)Irrational Roots
  •   (a)81 (b)Real (c)Not Equal Roots (d)Irrational Roots

  • 10) Quadratic Equation 2x² + 3x -8 = 0 Find the (a) Discriminant, (b) Real or Not Real Roots, (c) Equal (one) or Unequal Roots, (d) Rational or Irrational Roots?

  •   (a)73 (b)Real (c)Not Equal Roots (d)Irrational Roots
  •   (a)83 (b)Not Real (c)Equal Roots (d)Rational Roots
  •   (a)13 (b)Not Real (c)Equal Roots (d)Irrational Roots
  •   (a)13 (b)Real (c)Equal Roots (d)Rational Roots

  • 11) Quadratic Equation b² - 4ac > 0 Find the Real or Not Real Roots and Equal (one) or Unequal Roots?

  •   Not Real,Not equal Roots
  •   Not Real,Equal Roots
  •   Real,Equal Roots
  •   Real,Not equal Roots

  • 12) Quadratic Equation b² - 4ac = 0 Find the (a) Real or Not Real Roots, (b) Equal (one) or Unequal Roots?

  •   (a)Real (b)Equal
  •   (a)Real (b)Not Equal
  •   (a)Not Real (b)Not Equal Roots
  •   (a)Not Real (b)Equal

  • 13) Quadratic Equation b² - 4ac < 0 Find the Real or Not Real Roots

  •   Real
  •   Equal Roots
  •   Not Real
  •   None of these

  • 14) Quadratic Equation b² - 4ac is a perfect square the roots. Find the (a) Real or Not Real Roots (b) Equal (one) or Unequal Roots (c) Rational or Irrational Roots?

  •   (a)Real (b)Not equal (c)Rational Roots
  •   (a)Real (b)Equal (c)Irrational Roots
  •   (a)Not Real (b)Equal (c)Irrational Roots
  •   (a)Real (b)Equal (c)Rational Roots

  • 15) Find the number of roots the following equations x² + 5x + 6 = 0

  •   One real roots
  •   No real roots
  •   Two real roots
  •   Irrational roots

  • 16) Find the number of roots the following equations x² + x + 1 = 0?

  •   Two real roots
  •   One non real roots
  •   Two non real roots
  •   No roots

  • 17) Find the number of roots the following equations x² − 2x + 3 = 0?

  •   Two non real roots
  •   One non real roots
  •   One real roots
  •   Two real roots

  • 18) Find the number of roots the following equations x² − 2x − 3 = 0?

  •   One real roots
  •   Two real roots
  •   One non real roots
  •   No roots

  • 19) Find the number of roots the following equations 2x² − 3x + 3 = 1?

  •   One non real roots
  •   Two non real roots
  •   One real roots
  •   No roots

  • 20) Find the number of roots the following equations: x² + 6x + 9 = 0 ?

  •   One non real roots
  •   Two real roots
  •   Two non real roots
  •   One real roots

  • 21) Show that the line y = 1 - x does not intersect with the graph of the curve y = x² + x + 3.

  •   No real roots
  •   Irrational roots
  •   One real root
  •   Real roots

  • 22) Show that the line y = 2 - x does not intersect with the graph of the curve y = 3/ x ?

  •   Irrational roots
  •   Equal roots
  •   Real roots
  •   No real roots

  • 23) Show that the line y = 4 - x intersects with the graph of the curve y = 4/x at one point only

  •   No real roots
  •   Two real roots
  •   Irrational roots
  •   One real root

  • 24) Show that the line y = x intersects with the graph of the curve y = 9 / 6 - x at one point only

  •   One non real roots
  •   One real root
  •   Two real root
  •   Two non real roots

  • 25) Show that the function y = 3x² - 5x + 4 is always positive for any value of x?

  •   1
  •   No real solution
  •   2
  •   0

  • 26) Find the range of values t can take for the equation 9x² + tx + 4 = 0 to have two distinct real roots.

  •   t < -16 or t >16
  •   t < -15 or t >15
  •   t < -10 or t >10
  •   t < -12 or t >12

  • 27) Find the range, or ranges, of values K can take for the equation Kx²− 4x + (5 − K) = 0 to have 2 distinct real roots.

  •   K < 5 or K > 5
  •   K < 2 or K > 2
  •   K < 7 or K > 7
  •   K < 1 or K > 4

  • 28) Find the range(s) of values b can take for 9x² + bx + 4 = 0 to have 2 real distinct roots

  •   b < -10 or b > 10
  •   < -12 or b > 12
  •   b < -9 or b > 9
  •   b < -11 or b > 11

  • 29) Find the range(s) of values k can take for x² + (k + 1)x + 1 = 0 to have 2 distinct roots.

  •   k < -5 or k > 3
  •   k < 9 or k > 5
  •   k < -3 or k > 1
  •   k < 1 or k > 1

  • 30) Find the range(s) of values k can take for 2x² + (3 - k)x + k + 3 = 0 to have 2 real distinct roots.

  •   k < -1 or k > 11
  •   k < -3 or k > 12
  •   k < -1 or k > 15
  •   k < -3 or k > 10
Answer Key
Maths
S.No Topic Name Date Online Offline
1 LQE Model 12-February
2 Interpreting Functions 11-February
3 Vector and Matrix Quantities 10-February
4 Complex Number 09-February
5 Quantity 08-February
6 Real Number System 05-February
7 Number Sense - Polynomials 03-February
8 Algebra 02-February
9 Quadratic Functions 01-February