For what values of b does the equation  have complex roots. 4x^2 - bx + 16 = 0

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The roots of a quadratic equation of the form ax^2 + bx + c = 0 are `(-b+-sqrt(b^2 - 4ac))/(2a)` . The roots are complex if b^2 - 4ac < 0.

For the equation 4x^2 - bx + 16 = 0, the roots are complex when `b^2 - 4*4*16 < 0`

=> `b^2 < 256`

=> b < 16 and b > -16

The roots of the equation 4x^2 - bx + 16 = 0 are complex if -16<b<16.

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aruv | High School Teacher | (Level 2) Valedictorian

Posted on

If you have quadratic equation

`ax^2+bx+c=0`

it has complex roots if

`D=b^2-4ac<0`

your problem is

`4x^2-bx+16=0`

`a=4,c=16`

`(-b)^2-4.4.16<0`

`b^2-256<0`

`b^2<256=16^2`

`b<16`

`or`

`-b<16`

`b> -16`

Answer` <br> `

`-16<b<16`

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