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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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