Q3 of 108 Page 44

Find these values of k for which the roots of the following quadratic equations are real and distinct:

x2 – kx + 9 = 0


When we compare the above quadratic equation with the generalized one we get,

ax2 + bx + c = 0


a = 1


b = -k


c = 9


Since the quadratic equations have real and distinct roots,


b2 – 4ac > 0 for real and distinct roots


⟹ (-k) 2 – (4 × 9 × 1) > 0


⟹ k 2 – 36 > 0


⟹ k 2 > 36


⟹ k > ± 6


Which implies k < -6 and k > 6.


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