Question

Class 10 maths quadratic equations summary

Answer 1

An equation in the form of ax^2 + bx + c =0 is called as a quadratic equation.
It has two roots.
Both of them maybe real,equal or unreal. It can be found out through the discriminant of the parabola formula b^2 - 4ac.
if it's value is less than zero...the the roots are unreal. if it's more than zero..they arey real.if it is equal to zero..then the roots are equal.
The roots of a given quadratic equation can be found through factorisation, completing square or formula method.
The forrmula to find roots of a quadratic equation is
-b +/- √(b^2-4ac)
_____________
2a



Hope it helps u!

Answer 2

Answer:

A quadratic polynomial of the form ax² + bx + c, where a ≠ 0 and a, b, c are real numbers, is called a quadratic equation

when ax² + bx + c = 0.

Here a and b are the coefficients of x² and x respectively and ‘c’ is a constant term.

Any value is a solution of a quadratic equation if and only if it satisfies the quadratic equation.

Quadratic formula: The roots, i.e., α and β of a quadratic equation ax² + bx + c = 0 are given

by −b±D√2a or −b±b2−4ac√2a provided b² – 4ac ≥ 0.

Here, the value b² – 4ac is known as the discriminant and is generally denoted by D. ‘D’ helps us to determine the nature of roots for a given quadratic equation. Thus D = b² – 4ac.

Step-by-step explanation:

The rules are:

If D = 0 ⇒ The roots are Real and Equal.If D > 0 ⇒ The two roots are Real and Unequal.If D < 0 ⇒ No Real roots exist.

If α and β are the roots of the quadratic equation, then Quadratic equation is x² – (α + β) x + αβ = 0 Or x² – (sum of roots) x + product of roots = 0

where, Sum of roots (α + β) = −coefficientofxcoefficientofx2=−ba