Maths Discriminant Hard Question

Hi guys, I’m having trouble with this question. Can someone help me thank you so much if you do !!

What condition needs to be satisfied to have real roots?

b^2-4ac
Substitute the values and you get K^2+16.
B)square root of K^2+16 = k+4
And since we are told in question that k is a real number the discriminant is positive and if the discriminant is greater than 0, then there are 2 different real roots, thus answering the question.

It doesn’t give any values though; it’s a proof question so surely it’d require algebra ?

For distinct real roots, we require that $b^2 - 4ac > 0$ i.e. $b^2 > 4ac$. Since we are given $a,c$ then we know what $4ac$ is. Do you understand why we can always pick a value of $b$ so that its square is strictly bigger than 4ac ?

Would this be enough for full marks in an A level exam?

The discriminant must be equal to or greater than 0 ?