Nature of roots and relation between roots and coefficients of quadratic equation. Mathematics State Board, Class 10: lessons, tests, tasks.

1.	Nature of roots
2.	Some example problems based on nature of roots

1.	Multiple choice question Difficulty: easy	1
2.	Two mark example problem I Difficulty: easy	2
3.	Two mark example problem II Difficulty: easy	2
4.	Two mark example problem III Difficulty: easy	2
5.	Two mark example problem IV Difficulty: easy	12
6.	Two mark example problem III Difficulty: easy	4
7.	Two mark exercise problem I Difficulty: easy	2
8.	Two mark exercise problem II Difficulty: easy	2
9.	Two mark exercise problem IV Difficulty: easy	2
10.	Two mark exercise problem V Difficulty: easy	2
11.	Two mark exercise problem V Difficulty: easy	2
12.	Two mark exercise problem VI Difficulty: medium	6
13.	Two mark exercise problem IV Difficulty: medium	2
14.	Two mark exercise problem IV Difficulty: medium	2
15.	Five mark example problem I Difficulty: medium	5
16.	Five mark example problem II Difficulty: medium	5
17.	Five mark example problem III Difficulty: medium	5
18.	Five mark example problem IV Difficulty: medium	5
19.	Five mark example problem V Difficulty: medium	15
20.	Five mark exercise problem VI Difficulty: medium	5
21.	Five mark exercise problem VII Difficulty: medium	5
22.	Five mark exercise problem VIII Difficulty: medium	5
23.	Five mark exercise problem IX Difficulty: medium	5
24.	Five mark exercise problem X Difficulty: hard	5
25.	Five mark exercise problem XI Difficulty: hard	5
26.	Five mark exercise problem XII Difficulty: hard	10
27.	Five mark exercise problem XIII Difficulty: hard	5
28.	Five mark exercise problem XIV Difficulty: hard	5
29.	Five mark exercise problem XV Difficulty: hard	5
30.	Five mark exercise problem XVI Difficulty: hard	5

1.	Find the nature of the roots of the quadratic equations Difficulty: easy	2
2.	Find the discriminant of the quadratic equations Difficulty: easy	2
3.	Determine the possibility of the given situation Difficulty: easy	2
4.	Identify the quadratic equation Difficulty: easy	2
5.	Find the discriminant and its nature of roots Difficulty: medium	2
6.	Find the value(s) of 'k' for distinct roots of the equation Difficulty: medium	2
7.	Find the nature of roots and determine them if its real. Difficulty: medium	2
8.	Find the roots of the quadratic equation Difficulty: medium	2
9.	Feed me! Difficulty: medium	2
10.	Make the given expression in terms of α + β and αβ Difficulty: medium	2
11.	Find the value of the given expressions Difficulty: medium	5
12.	Find the value of 'p' and the roots of the equation Difficulty: hard	5
13.	Find the integers if the situation is possible Difficulty: hard	5
14.	Find the possibility of the given situation Difficulty: hard	5
15.	Case study: Nature of roots Difficulty: hard	5
16.	Verify the relation between roots and coefficients of the quadratic equation Difficulty: hard	5
17.	Find the quadratic equations for the given roots Difficulty: hard	5
18.	Find the value of 't' and the roots of the equation Difficulty: hard	5

1.	Find the value of 'k' Difficulty: easy	1
2.	Determine the value Difficulty: medium	2
3.	Prove the following Difficulty: medium	0
4.	Form a quadratic equation Difficulty: hard	5

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Methodical recommendation

Nature of roots and relation between roots and coefficients of quadratic equation