Question

I tried doing this problem and this is the problem

if a, b, and c are real numbers and \[a+bx+cx^2 \geq 0\] for any real number x, explain why \[b^2-4ac \leq 0\]

this is how i am trying to do if we know \[a +bx+cx^2 \geq 0\] then our disriminant is \[\sqrt{b^2 - 4ca}\]but this cant be \[\leq o\] because it would make our square root negative. and that woulnd exist so the solution wouldnt exist.

I am confused on this please help out, if you could give me some hints or a solution i would be happy, these are just practice questions i need help on

Answer 1

It's\[ax^{2} + bx + c\]but you're nearly there ! :-)

For a positive value of a, then if the discriminant is negative the curve must lie completely above the horizontal axis that is, no solutions exist for \[ax^{2} + bx + c = 0\]if the discriminant is equal to zero then one solution exists and the curve touches the axis at one point only.