**Properties of quadratic equations :**

Here we are going to see the properties of quadratic equations which would be much useful to the students who practice problems on quadratic functions.

1. The zeros of a quadratic function f(x) = ax²+bx+c are nothing but the two values of "x" when f(x) = 0 or ax² + bx +c = 0.

Here,

**"ax² + bx +c = 0" is called as quadratic equation**

Finding the two zeros of a quadratic function or solving the quadratic equation are the same thing.

3. There are three methods to find the two zeros of a quadratic equations.

They are,

(i) Factoring

(ii) Quadratic formula

(iii) Completing square

4. If the two zeros of a quadratic equation are irrational, then the two zeros (roots) will occur in conjugate pairs. That is, if (m+√n)is a root, then (m-√n) is the other root of the same equation.

5. The sum of the zeros of the quadratic equation ax²+bx+c = 0 is -b/a

6. The product of the zeros of the quadratic equation ax²+bx+c = 0 is c/a

7. If one zero is reciprocal to the other root then their product c/a = 1 or c = a.

8. If one zero is equal to other root but opposite in sign then their -b/a = 0 or b = 0.

9. If we know the two roots of a quadratic equation, we can use the following formula to form the quadratic equation.

x² - (Sum of the roots)x + product of the roots = 0

10. The graph of any quadratic equation will be a parabola.

11. The zeros of a quadratic equation are the x-coordinates of the points where the parabola (graph of quadratic a function) cuts x-axis.

12. If the two zeros of a quadratic function are imaginary, then the graph (parabola) will never intersect x - axis.

13. The two x-intercepts of a parabola (graph of a quadratic function) are nothing but the zeros of the quadratic function.

14. x- coordinate of the vertex of the parabola is -b/2a and the vertex is [ -b/2a, f(-b/2a) ]

15. To know at where the parabola cuts y-axis or y-intercept of the parabola, we have to plug x = 0 in the given quadratic function.

16. f(x) = ax² + bx + c, if the sign of the first term (ax²) is negative, the parabola will be open downward. Otherwise, the parabola will be open downward.

17. The discriminant b² - 4ac discriminates the nature of the zeros of the quadratic equation ax² + bx + c = 0.

Let us see how this discriminant **"b****² - 4ac" **can be used to know the nature of the roots of a quadratic equation.

After having gone through the stuff given above, we hope that the students would have understood "Properties of quadratic equations".

Apart from the stuff given above, if you want to know more about "Properties of quadratic-equations", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**