Question

Answer this question please​

Answer 1

Answer:

k<4

Step-by-step explanation:

For which values of k does the equation x2−4x+k=0 have distinct real roots?

For which values of k does the equation x2−4x+k=0 have distinct real roots?

Let's solve it with the usual quadratic formula, thus we have,

x=4±16−4k−−−−−−√2 .

We observe that for x to be real this term right here 16−4k−−−−−−√ normally referred to as the discriminant of the equation has to be real after all the other terms in the expression are real.

So for which values is the discriminant real? We recall that the square root can only be real if the term under the root sign is nonnegative, otherwise we will be dealing with Complex numbers. So we have that 16−4k≥0 for x to be real.

But of course the question is asking for distinct real roots. We know that 0 is the only number when added to or subtracted from a given number we get the same number. With this knowledge we have that for the roots of the equation to be distinct the only nonnegative number the discriminant has to avoid is 0 . This can only happen when 16−4k>0 which is equivalent to k<4 and we have our solution. The roots of the equation can only be distinct real numbers when k<4 .