Question

if the quadratic expression px^2+qx+r has the same sign as that of p ,then find the relation among p,q and r.

Answer 1

Given: The equation: px^2 + qx + r

To find: If the quadratic expression px^2+qx+r has the same sign as that of p ,then find the relation among p,q and r.

Solution:

• Now we have given the equation:

                    f(x) = px^2 + qx + r

• If p>0, then px^2 + qx + r > 0 for x∈R if :

                    Discriminant < 0  

                    b² - 4ac < 0

• If p<0, then px^2 + qx + r < 0 for x∈R if:

                    Discriminant < 0

                    b² - 4ac < 0

• Now we can see that in both cases discriminant is less than 0.

• So, the equation px^2+qx+r has the same sign as that of p if Discriminant < 0 , that means:

                    q^2 - 4pr < 0

                    q^2 < 4pr

Answer:

                So the relation is: q^2 < 4pr