Question

let ALPHA and BETA be the roots of the quadratic equation x^2-px-4=0,where p is a real constant.
How to prove that the roots ALPHA and BETA are real and distinct?

Answer 1

Answer:

If discriminant of a quadratic equation is positive then roots ALPHA and BETA are real and distinct

Step-by-step explanation:

It is given that,

Let ALPHA and BETA be the roots of the quadratic equation x^2-px-4=0,where p is a real constant.

To find the nature of roots we have to find the discriminant(b^2 - 4ac) of equation

Here the quadratic equation be x^2-px-4=0,where p is a real constant.

Coefficients of equation

a = 1

b = -p

c = -4

To find the discriminant

b^2 - 4ac = (-p)^2 - 4 x 1 x -4 = p^2 + 16 which is a positive number.

therefore root of discriminant is a positive .

So roots ALPHA and BETA are real and distinct