Notes
IIT Madras
Mathematics 🧮
Activity Questions 3.7

Activity Questions 3.7

Question 1

Choose the correct standard form of a quadratic equation with roots $\frac{2}{3}$ and $\frac{10}{3}$.

Multiple choice options:

  • $6x^2 - x - 70 = 0$
  • $\frac{1}{3}(6x^2 - x - 70) = 0$
  • $\frac{1}{6}(6x^2 - x - 7) = 0$
  • $(x - \frac{2}{3})(x + \frac{10}{3}) = 0$

Solution

Question 2

Choose the correct option about a with the help of Figure AQ-5.1.

The question includes a graph showing a parabola with the equation $y = a(x + 2)(b - x)$. The graph shows an upward-opening parabola with x-intercepts at $(-2, 0)$ and $(b, 0)$.

Multiple choice options:

  • $a > 0$
  • $a = 5$
  • $a = 0$
  • $a < 0$

Solution

Both questions focus on quadratic equations - the first on converting from factored form with given roots to standard form, and the second on determining the sign of the leading coefficient based on the parabola’s orientation in a graph.

Multiple Select Questions (MSQ):

Question 3

Choose the set of correct options regarding quadratic functions $p(x) = x^2 - 7x + 10$ and $q(x) = x^2 + 7x + 10$.

Multiple select options (checkboxes):

  • $p(x)$ has two roots -5 and -2
  • $p(x)$ has two roots 5 and 2
  • $q(x)$ has two roots 5 and 2
  • $q(x)$ has two roots -5 and -2

Solution

Question 4

Identify the incorrect options for the quadratic equation $x^2 - 15x + 54 = 0$.

Multiple select options (checkboxes):

  • 9 is a root
  • Both the roots are equal
  • There are no roots
  • 6 is a root

Solution

Both questions are Multiple Select Questions (MSQ) that require students to identify multiple correct or incorrect statements about quadratic equations, testing their understanding of finding roots and analyzing properties of quadratic functions.

Summary Lecture (Quadratic Functions)Solution of quadratic equation using Factorization

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