Nature of Roots of Quadratic Equation Discriminant Worksheet :
Here we are going to see some example practice questions on nature of roots of quadratic equation.
(1) Determine the nature of the roots for the following quadratic equations
(i) 15x2 + 11x + 2 = 0 Solution
(ii) x2 − x − 1 = 0 Solution
(iii) √2t2 −3t + 3√2 = 0 Solution
(iv) 9y2 − 6√2 y + 2 = 0 Solution
(v) 9a2b2x2 −24abcdx + 16c2d2 = 0 , a ≠ 0 , b ≠ 0
(2) Find the value(s) of ‘k’ for which the roots of the following equations are real and equal.
(i) (5k −6)x2 + 2kx + 1 = 0 Solution
(ii) kx2 +(6k + 2)x + 16 = 0 Solution
(3) If the roots of (a −b)x2 + (b −c)x + (c −a) = 0 are real and equal, then prove that b, a, c are in arithmetic progression Solution
(4) If a, b are real then show that the roots of the equation (a − b)x2 −6(a +b)x −9(a − b) = 0 are real and unequal. Solution
(5) If the roots of the equation (c2 −ab)x2 −2(a2 −bc)x +b2 −ac = 0 are real and equal prove that either a = 0 (or) a3 +b3 +c3= 3abc Solution
After having gone through the stuff given above, we hope that the students would have understood, "Find Unknowns in Quadratic Equation with Alpha Beta".
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