## use the discrminant to determine all values of k which would result in the equation -3x^2-6x+k=0 having real,unequal roots.​ must be right t

Question

use the discrminant to determine all values of k which would result in the equation -3x^2-6x+k=0 having real,unequal roots.​ must be right ty helppp asap

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1 year 2021-08-18T17:31:44+00:00 1 Answers 0 views 0

[tex]k>-3[/tex]

Step-by-step explanation:

We have the equation:

[tex]-3x^2-6x+k=0[/tex]

Where a = -3, b = -6, and c = k.

And we want to determine values of k such that the equation will have real, unequal roots.

In order for a quadratic equation to have real, unequal roots, the discriminant must be a real number greater than 0. Therefore:

[tex]b^2-4ac>0[/tex]

Substitute:

[tex](-6)^2-4(-3)(k)>0[/tex]

Simplify:

[tex]36+12k>0[/tex]

Solve for k:

[tex]12k > -36[/tex]

[tex]k>-3[/tex]

So, for all k greater than -3, our quadratic equation will have two real, unequal roots.

Notes:

If k is equal to -3, then we have two equal roots.

And if k is less than -3, then we have two complex roots.