Question

if x2+5px+16 has no real roots then
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Answer 1

If the discriminant of a quadratic function is less than zero, that function has no real roots, and the parabola it represents does not intersect the x-axis.

Answer 2

$\sf{Answer}$

Step by step explanation :-

As they given x²+5px +16 has no real roots So,

b²-4ac<0

x² +5px +16

a = 1

b = 5p

c = 16

So, (5p)² -4(1)(16) <0

25p² -64 <0

25p² < 64

p² < 64/25

p² < (8/5)²

p < 8/5

p < 1.6

So, Required values of p are

P should be less than the value of 1.6

So, p = 1,0,1.5,1.4 etc .........<1.6

Concept to know:-

Nature of roots is determined by Discriminant

Discriminant is denoted by D

Cases :-

If D<0 roots are not real &conjugate to each other

D>0 roots are real & distinct

D=0 roots are equal and real

D>0 & D is perfect square roots are rational and distint

D<0 &D is not perfect square roots are irrational and conjugate