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Subjects
Mathematics State Board
Class 10
Algebra
Nature of roots and relation between roots and coefficients of quadratic equation

15. Case study: Nature of roots

Exercise condition:

5 m.

Dheeraj and Roshan went to a nearby pizza shop for lunch. The shop had a unique method for the price allotment of pizza daily. The price of each pizza they prepare on a specific day equals 4, more than thrice the total number of pizzas they produce on that day. The total cost of production on that day was 480 rupees.

1. The quadratic equation for the given situation is:

$3 x^{2} + 4 x - 480 = 0$
$3 x^{2} + 4 x + 480 = 0$
$3 x^{2} - 4 x + 480 = 0$
$3 x^{2} - 4 x - 480 = 0$

2. Find the number of pizzas produced.

12
13
10
15

3. Find the cost of each pizza.

39
40
43
35

4. The general form of the quadratic equation:

\(ax^2 - bx + c = 0\)
\(ax^2 + bx = c\)
\(ax^2 + bx + c = 0\)
\(ax^2 + ax + c = 0\)

5. If the nature of roots are real and equal, then:

\(b^2 - 4ac > 0\)
\(b^2 - 4ac = 0\)
\(b^2 - 4ac \le 0\)
\(b^2 - 4ac < 0\)

Reference:

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