Question

determine the nature of roots for the quadratic equation ​

Answer 1

Answer:

We will discuss here about the different cases of discriminant to understand the nature of the roots of a quadratic equation.

We know that α and β are the roots of the general form of the quadratic equation ax2 + bx + c = 0 (a ≠ 0) .................... (i) then we get

α = −b−b2−4ac√2a and β = −b+b2−4ac√2a

Here a, b and c are real and rational.

Then, the nature of the roots α and β of equation ax2 + bx + c = 0 depends on the quantity or expression i.e., (b2 - 4ac) under the square root sign.

Thus the expression (b2 - 4ac) is called the discriminant of the quadratic equation ax2 + bx + c = 0.

Answer 2

Answer:

b square _ 4ac =0 real and equal

b square _ 4ac >o real and unequal

b square - 4ac <0 imaginary and complex