Question

For what value(s) of k will the function y=6x^2-8x+k have: a) one zero b) two zeros c) no zeros *this is not multiple choice*

Answer 1

Explanation:

Hello, please consider the following.

`6x^2-8x+k=0\\\\\text{We compute the discriminant.}\\\\\Delta = b^2-4ac=8^2-4*6*k=8*8-8*3*k=8*(8-3k)`

And the we know that if the discriminant is

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`\Delta` < 0, meaning 8-3k<0, meaning

`\boxed{k>(8)/(3)}`

then, there is no real solution.

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`\Delta = 0`, meaning

`\boxed{k=(8)/(3)}`

There is 1 solution.

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`\Delta` > 0, meaning

`\boxed{k<(8)/(3)}`

There are 2 solutions.

Thank you

PS: To give more details...

`8-3k=0\\\\\text{Add 3k}\\\\8=3k\\\\\text{Divide by 3}\\\\k=(8)/(3)`