#### Question

Find the values of *k* for which the given quadratic equation has real and distinct roots:

kx^{2} + 6x + 1 = 0

#### Solution

The given quadric equation is kx^{2} + 6x + 1 = 0, and roots are real and distinct.

Then find the value of *k.*

Here,

a = k, b = 6 and c = 1

As we know that D = b^{2} - 4ac

Putting the value of a = k, b = 6 and c = 1

D = (6)^{2} - 4 x (k) x (1)

= 36 - 4k

The given equation will have real and distinct roots, if D > 0

36 - 4k > 0

Now factorizing of the above equation

36 - 4k > 0

4k < 36

k < 36/4

k < 9

Now according to question, the value of *k* less than 9

Therefore, the value of k < 9.

Is there an error in this question or solution?

#### APPEARS IN

Solution Find the Values Of K For Which the Given Quadratic Equation Has Real and Distinct Roots: Kx2 + 6x + 1 = 0 Concept: Nature of Roots.