Question

Questions:
1. When do you say that the roots of a quadratic equation are real or not real?
2. When do you say that the roots of a quadratic equation are rational or
irrational?
3. When do you say that the roots of a quadratic equation are equal or not
equal?​

Answer 1

Answer:

1. If the discriminant of a quadratic equation is less than zero, that equation has no real roots.

2. The solution to a quadratic equation is rational if some integer x, because the square root of a perfect square is rational, but the square root of a non-perfect square is irrational.

3. When the quadratic is equated to zero, that is called a “quadratic equation” and the two values of the variable x for which the quadratic is equal to zero are called the “roots”.

Answer 2

Given :   Quadratic Equations

To Find :  Condition for Nature of  the roots:

Real or not real

Rational or irrational

Roots equal or not

Solution:

Quadratic equation is of the form ax²+bx+c=0  where a  , b and c are real also  a≠0.

D =  b²-4ac is called discriminant.

D >0 roots are real and distinct

D =0 roots are real and equal

D < 0 roots are imaginary ( not real ) and different

Real or not real   :

D ≥ 0 , Roots are Real

D < 0 , Roots not real

Rational or irrational

Rational : Roots are Rational if a , b and c are rational and D is a perfect square , otherwise irrational

Roots equal or not

D = 0 Roots are equal

D  ≠ 0 , Roots are not equal

Learn More:

if alpha +beta are the roots of equation 4x²-5x+2=0 find the equation ..

brainly.in/question/8333453

obtain all the zeros of the polynomial 8x^4+8x^3-18x^2-20x-5 if two ...

brainly.in/question/7286826

If two zeroes of a polynomial p(x) = x4 – 5x3 – x2 + 35x – 42 are 2 and

brainly.in/question/17304050