Question

By completing the square express the inequality r? +8x+c >0 in the form fx+al > b where a and b are constants. Therefore, find the interval of x so that x² +8x +10 is always more than 3.​

Answer 1

Answer:

The given equation can be written as

x

2

−8x+a

2

−6a=0

Since the roots of the above equation are real,

∴B

2

−4AC≥0⇒64−4(a

2

−6a)≥0

⇒a

2

−6a−16≤0

⇒(a+2)(a−8)≤0

⇒a ϵ [−2,8]