Q3 of 108 Page 44

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

kx2 + 6x + 1


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

ax2 + bx + c = 0


a = k


b = 6


c = 1


Since the quadratic equations have real and distinct roots,


b2 – 4ac > 0 for real and distinct roots


⟹ (6)2 – (4 × k × 1) > 0


⟹ 36 – 4k > 0


⟹ 4k < 36 [Dividing both sides by 4]


⟹ k < 9


More from this chapter

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2

Find that value of k in the following quadratic equation whose roots are real and equal:

kx2 – 5x + k = 0


 3

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

kx2 + 2x + 1 = 0


 3

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

x2 – kx + 9 = 0


 4

Find those values of k for which the roots of the equation x2 + 5kx + 16 = 0 are not real.