Question

1. Determine p so that the equation x 2 + 5px + 16 = 0 has no real roots.

Answer 1

D must be less than 0 than solve the equation and get answer

Answer 2

Given quadratic equation is=x² + 5px +16 = 0

On comparing with standard form of quadratic equation i.e ax² + bx + c =0,

Here, a = 1 , b= 5p, c= 16

D(discriminant)= b²-4ac

= (5p)² - 4× 1 × 16

= 25p² - 64

Since, roots of given equation has no real roots.  D < 0.

25p² - 64 <0

5p² - 8² < 0

(5p +8)(5p -8)< 0         [ a² - b² = (a-b)(a+b)]

5p +8 <0 or 5p - 8< 0

p > -8/5 or p < 8/5

-8/5 < p  < 8/5

So the value of p would lie between -8/5 and 8/5

HOPE THIS WILL HELP YOU...