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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: 13x2-7x+1 = 0(7+Ö3i)/26, (7-Ö3i)/26-1+i, -1-i2+i, 2-i Q 2: Ö3x+1 - Öx-1 = 25, 1-5, -1-5, 1 Q 3: 9x2+10x+3 = 01, -1-5/9+Ö2/9i, -5/9-Ö2/9i-2i, -2i Q 4: 2x2-2Ö3x+1 = 0 (Ö3+Ö5i)/, (7, 45, 1 Q 5: 2y2 - 5y -3 = 03,1/23, -1/2-3, -1/2 Q 6: x2-7ix-12 = 03i, 4i3i, 5i3,4 Q 7: 25x2-30x+9 = 03/5,3/55,13/5+Ö2/5i, 3/5-Ö2/5i Q 8: 8x2+9x+3 = 0i-3, 52, i-9/16+Ö15i/16, -9/16-Ö15i/16 Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!