Question

If the quadratic equation 12x^2-2bx+9=0 has no real roots,then which of the following is always true:-
1)b is smaller than-6√3
2)b is greater than-6√3
3)-6√3 is smaller than b is smaller than 6√3 4)b Smaller than-6√3 and b is greater than 6√3

Answer 1

Given :   12x² - 2bx  + 9  = 0  Has no Real roots  

To find : which of the following is always true

Solution:

12x² - 2bx  + 9  = 0

Has no Real roots

=>  (-2b)²  - 4(12)(9)  <  0

=> 4b²  - 4*108 < 0

=> b² - 108 < 0

=> b² < 108

=>    - √108  <  b  < √108

=>    -6√3 < b < 6√3

-6√3 is smaller than b is smaller than 6√3

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