Question

EXERCISE - 5.4
Find the nature of the roots of the following quadratic equations. If real roots exist, find
them
(0)56
© 2x2 - 3x + 5 = 0
3r? - 413x + 4 = 0
2x² - 6x + 3=0
Find the values of k for each of the following quadratic equations, so that they have two
equal roots.
0 212 + lax + 3 = 0
lor (x - 2) + 6 = 0 (k = 0)
3. Is it possible to design a rectangular mango grove whose length is twice its breadth, and the
area is 800 mº? If so, find its length and breadth.
The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in
years was 48. Is the above situation possible? If so, determine their present ages,
5. Is it possible to design a rectangular park of perimeter 80 m and area 400 m²? If so, find
its length and breadth. Comment on you answer.
4​

Answer 1

Step-by-step explanation:

⇒2(l+b)=80

⇒l+b=40

∴b=40−l --(1)

Substituting (1) in Area, we get

⇒l(40−l)=400

⇒40l−l

2

=400

⇒l

2

−40l+400=0

⇒(l−20)(l−20)=0

∴l=20

has equal roots, so it is possible to design the rectangle of given parameters.

⇒b=40−20=20

We now know that the length of the park is 20 m and the breadth of the park is also 20 m.