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### High School Mathematics - 212.8 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. If b2-4ac = 0, then each root of the equation becomes -b/2a and hence roots are real and equal. If b2-4ac is positive and a perfect square then, Öb2-4ac is rational and hence the roots of the equation are rational and unequal. If b2-4ac is positive but not a perfect square then, Öb2-4ac is real but irrational and hence the roots of the equation are irrational and unequal. If b2-4ac is negative and a perfect square then, Öb2-4ac 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: 2y2 - 5y -3 = 03, -1/23,1/2-3, -1/2 Q 2: 21x2-29x+11 = 0(-9+Ö3i)/42, (-9-Ö3i)/42Ö3-i, i2, i Q 3: x2-7ix-12 = 03i, 5i3,43i, 4i Q 4: 13x2-7x+1 = 02+i, 2-i-1+i, -1-i(7+Ö3i)/26, (7-Ö3i)/26 Q 5: Ö3x+1 - Öx-1 = 2-5, -1-5, 15, 1 Q 6: 9x2+10x+3 = 01, -1-5/9+Ö2/9i, -5/9-Ö2/9i-2i, -2i Q 7: 8x2+9x+3 = 0i-3, 5-9/16+Ö15i/16, -9/16-Ö15i/162, i Q 8: x2-(3Ö2-2i)x-6Ö2i = 0-5, -5ii+5, i-529/42+Ö83/42i, 29/42-Ö83/42i Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!