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

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

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

Q 4: 8x2+9x+3 = 0
-9/16+15i/16, -9/16-15i/16
i-3, 5
2, i

Q 5: 17x2-8x+1 = 0
-2+i, -2-i
i, -i
4/17+i/17, 4/17-i/17

Q 6: 2x2-23x+1 = 0
5, 1
7, 4
(3+5i)/, (
Q 7: 25x2-30x+9 = 0
5,1
3/5,3/5
3/5+2/5i, 3/5-2/5i

Q 8: 13x2-7x+1 = 0
(7+3i)/26, (7-3i)/26
2+i, 2-i
-1+i, -1-i

Question 9: This question is available to subscribers only!

Question 10: This question is available to subscribers only!


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