NATURE OF ROOTS OF QUADRATIC EQUATION DISCRIMINANT WORKSHEET

(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          

Solution

(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

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