#### Question

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

x^{2} - kx + 9 = 0

#### Solution

The given quadric equation is x^{2} - kx + 9 = 0, and roots are real and distinct

Then find the value of *k.*

Here,

a = 1, b = (-k) and c = 9

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

Putting the value of a = 1, b = (-k) and c = 9

D = (-k)^{2} - 4 x (1) x (9)

= k^{2} - 36

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

k^{2} - 36 > 0

Now factorizing of the above equation

k^{2} - 36 > 0

k^{2} > 36

`k>sqrt36=+-6`

k < -6 Or k > 6

Therefore, the value of k < -6 Or k > 6.

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: X2 - Kx + 9 = 0 Concept: Nature of Roots.