Question

Answer the attachment.

Answer 1

Answer:

Step-by-step explanation:

The solution of a quadratic equation is given by the following formula

x=−b±b2−4ac√2a

Here a=1, b=−2k, c=k2+k−5

Plugging these into the formula yields...

x=2k±4k2−4(k2+k−5)√2

Since roots are less than 5, hence

⟹2k±4k2−4(k2+k−5)√2<5

⟹2k±4k2−4k2−4k+20−−−−−−−−−−−−−−−−√<10

⟹±20−4k−−−−−−√<2(5−k)

Now, squaring both sides gives...

⟹20−4k<4(5−k)2

⟹5−k<(5−k)2

⟹5−k<25−10k+k2

⟹0<20−9k+k2

⟹k2−9k+20>0

⟹(k−5)(k−4)>0

Hence the solutions are k<4 and k>5

We can write them in interval notation as  (−∞,4)∪(5,∞)