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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

High School Mathematics - 2
12.8 Quadratic Equations - Discriminant

The roots of a quadratic equation whether equal, unequal or non-real depend upon the quantity b2-4ac. which is called discriminant.
  1. If b2-4ac = 0, then each root of the equation becomes -b/2a and hence roots are real and equal.
  2. If b2-4ac is positive and a perfect square then, b2-4ac is rational and hence the roots of the equation are rational and unequal.
  3. If b2-4ac is positive but not a perfect square then, b2-4ac is real but irrational and hence the roots of the equation are irrational and unequal.
  4. If b2-4ac is negative and a perfect square then, b2-4ac is imaginary and hence no real roots exist.
We further observe that sum of two roots in any case is -b/a and product is c/a.


Directions: Solve the following.
Q 1: 9x2+10x+3 = 0
-2i, -2i
-5/9+2/9i, -5/9-2/9i
1, -1

Q 2: x2-7ix-12 = 0
3,4
3i, 5i
3i, 4i

Q 3: 21x2-29x+11 = 0
2, i
3-i, i
(-9+3i)/42, (-9-3i)/42

Q 4: 3x+1 - x-1 = 2
-5, 1
5, 1
-5, -1

Q 5: 4x2 + 4x = 3
-1/2, -3/2
1/2, -3/2
1/2, 3/2

Q 6: 25x2-30x+9 = 0
3/5,3/5
5,1
3/5+2/5i, 3/5-2/5i

Q 7: 2y2 - 5y -3 = 0
3,1/2
-3, -1/2
3, -1/2

Q 8: x2-(32-2i)x-62i = 0
i+5, i-5
-5, -5i
29/42+83/42i, 29/42-83/42i

Question 9: This question is available to subscribers only!

Question 10: This question is available to subscribers only!


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