Question

the condition for polynomials equetion ax squre + bx + c = 0 to be quadratic is

Answer 1

The condition for it to be quadratic is ax^2+bx+c=0.
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.
Generally we denote discriminant of the quadratic equation by ‘∆ ‘ or ‘D’.

Therefore,

Discriminant ∆ = b2 - 4ac

Depending on the discriminant we shall discuss the following cases about the nature of roots α and β of the quadratic equation ax2 + bx + c = 0.

When a, b and c are real numbers, a ≠ 0

Answer 2

$\alpha + \beta = - b \div a \\ \alpha \times \beta = c \div a$