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Find the Values Of K For Which the Given Quadratic Equation Has Real and Distinct Roots: X2 - Kx + 9 = 0 - CBSE Class 10 - Mathematics

Question

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

x2 - kx + 9 = 0

Solution

The given quadric equation is x2 - 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 = b2 - 4ac

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

D = (-k)2 - 4 x (1) x (9)

= k2 - 36

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

k2 - 36 > 0

Now factorizing of the above equation

k2 - 36 > 0

k2  > 36

k>sqrt36=+-6

k < -6 Or k > 6

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

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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.
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