Question

if α β are the roots of x²-px+q=0

Answer 1

Answer:

Step-by-step explanation:

The given quadratic equation is ;

x² + px + q = 0 .

Clearly,

a = 1

b = p

c = q

Also,

It is given that ,

α and ß are the roots of the given quadratic equation.

Thus,

Sum of roots = -b/a

α + ß = -p/1 = -p

Also,

Product of roots = c/a

αß = q/1 = q

Now,

Let A and B be the roots of required quadratic equation .

Also,

It is given that , (α - ß)² and (α + ß)² are the roots of the required quadratic equation .

Thus,

=> A = (α - ß)²

=> A = (α + ß)² - 4αß

=> A = (-p)² - 4q

=> A = p² - 4q

Answer 2

if α β are the roots of x²-px+q=0