Question

What is the probability that a quadratic equation p{x^2} + qx + r = 0 has distinct real roots if p,q and r are distinct and are taken from {1,5,6,8,9}?

Answer 1

Answer:

Answer

Given that,

px

2

+qx+r=0 p,q,r∈R

We know that if no real root then,

D<0

B

2

−4AC=0

⇒q

2

−4pr<0

⇒q

2

<4pr

Given function [f(x)=px

2

+qx+r=0]

If p>0

Put x=1 this function

f(1)=p+q+r>0

f(p+q+r)>0 has no real roots.

If p<0

Put f(1)=p+q+r<0

f(p+q+r)>0 has no real roots.

Hence it is complete solution.