Quadratic Equations: Nature of the Roots | CBSE MATH | Class 10 Chapter 4 Lesson 3

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[HarleenKaur-hhbf]

Homework Question :-
1) the discriminant of equation, 2x²-6x+3 is 12
Therfore, values of x is 3±root3/2.
2) We got the value of k as 0 and 6 and bcoz by the value 0 there will be no coefficient of x² and x therefore value of x is 6
3) Yes it is possible to design a Rectangle whose perimeter is 80m and area is 400m².
By finding discriminant = 0, we will automatically find that roots are real and equal and also x is 20.
It indicates that it is possible.
4) By making equation :- we got,
x²-8x+7
The factors were x-1 and x-7
If we do the square of 1, it cannot be the father's age
Therefore son's age is 7 years
Father's age is 7²= 49 years.
Thankyou mam for this exciting session 😊😊

[LakshiyaC]

HW 1.answer is 6
Kx²-2k+6=0
Discriminant is b²-4ac
(-2k)²-4(k)(6)=0
4k²-24k=0
4k²=24k
4k²/k=24k/k
4k=24
4k/4=24/4
k=6
2. Answer as 20 m

[TanmayAsija]

HOMEWORK QUESTION->
*Q1:* kx^2 + 2kx + 6 = 0
4k^2 - 24k = 0
4(k^2 - 6k) = 0
k^2 - 6k = 0 ---> By Hit and Trial Method *k=6*
*Q2:* 2(l+b)=40 or l+b = 40 or l = 40 - b
l x b = 400
(40 - b) b = 400
-b^2 + 40b - 400 = 0
*l = b = 20units*, ', It is a special Rectangle with equal sides or *Square*
*Q3:* Let the Old Age of the Child be x years;
A.T.Q --- New age of Father - Old Age of Father = 1
x^2 - 8x = 1 or x^2 - 8x - 1 = 0
x = *4 - root(17)* or *4 + root(17)*
Thank You Mam for the amazing session... By The Way, Homework Questions took alot of time...

[kalyaninithya]

1)Given quadratic equation: kx(x-2) +6
On simplying,
Kx²-2kx+ 6
Here, a= k, b= -2k and c = 6

Given that they have equal roots . So the discriminant must be equal to Zero .
D= b²-4ac
D= 4k²-4(k)(6)
D= 4k²-24k
As D= 0,
4(k²-6k)= 0
k²= 6k
k= 6k/k
k=6)

[geethanandinip]

The given quadratic equation is k x (x - 2) + 6 = 0.

This equation can be rewritten as
k
x
2
−
2
k
x
+



K = 0 or k = 6

But k cannot be 0, so the value of k is 6. First home work answer ha mam

[Prantajyoti-rvtv]

Ma'am, I have some question ❓
🔴 Are the circumference of all circle irrational as π is irrational and circumference of any circle is 2πr
🔴 Product of two same irrational number is rational (example: √2×√2=2). Then what is the value of π×π.
🔴 🏡📝
1) Given quadratic equation: kx(x-2) +6
On simplying,
Kx²-2kx+ 6
Here, a= k, b= -2k and c 6
Given that they have equal roots. So the discriminant must be equal to Zero.
D= b2-4ac
D= 4k²-4(k) (6)
D= 4k²-24k
As D= 0,
4(k²-6k)= 0
k²= 6k
k= 6k/k
k=6)

[geethanandinip]

Yes, it is possible to design a rectangular park of perimeter 80 m and area 400 m2. The length and breadth both are equal to 40 m.2nd question ka answer ha mam

[andreesclasses]

Hi mam I am Andree
Homework question:
1. D=4k^2-24k=0
k=6
2.b^2 -40b+400=0
Length=20m breadth= 20m
3.x^2-8x+7=0
Age of father =49
Age of son=7

[ForStudy-bk]

Thank u ❤ mam for this awesome session

[rajendarsiripuram]

Let the length and breadth of the park be l and b.

Perimeter of the rectangular park = 2 (l + b) = 80

So, l + b = 40

Or,  b = 40 – l

Area of the rectangular park = l×b = l(40 – l) = 40l – l2 = 400

l2 –  40l + 400 = 0, which is a quadratic equation.

Comparing the equation with ax2 + bx + c = 0, we get

a = 1,  b = -40,  c = 400

Since, Discriminant = b2 – 4ac

=(-40)2 – 4 × 400

= 1600 – 1600 = 0

Thus,  b2 – 4ac = 0

Therefore, this equation has equal real roots. Hence, the situation is possible.

The root of the equation,

l = –b/2a

l = -(-40)/2(1) = 40/2 = 20

Therefore, the length of the rectangular park,  l = 20 m

And the breadth of the park,  b = 40 – l = 40 – 20 = 20 m.

[AishaMaster-]

Homework question:-
Q1)General form,
kx²-2kx+6=0(given)
D=0; b²-4ac
=4k²-24k=0
4k²=24k
K²/k=6
Hence k=6.
Q2) by taking breath =x & length =400/x
Discriminate came out to be 0.
X=20.
Mam i Do not understand to solve last question plz help😊

[rajkumar-ukjn]

Homework Question :-
1) the discriminant of equation, 2x²-6x+3 is 12
Therfore, values of x is 3±root3/2.
2) We got the value of k as 0 and 6 and bcoz by the value 0 there will be no coefficient of x² and x therefore value of x is 6
3) Yes it is possible to design a Rectangle whose perimeter is 80m and area is 400m².
By finding discriminant = 0, we will automatically find that roots are real and equal and also x is 20.
It indicates that it is possible.
4) By making equation :- we got,
x²-8x+7
The factors were x-1 and x-7
If we do the square of 1, it cannot be the father's age
Therefore son's age is 7 years
Father's age is 7²= 49 years.

mam my name is kanishta

[omshree]

Yes it is possible to design a rectangular park. Here l=20b=2.

[geethanandinip]

present age of son is either
1
year or
7
years.3rd question ka answer ha mam

[Mahek]

Homework questions:-

1) roots are real and distriminate

2)k=6

3) length=40 breath=40

4) age of son =7
Age of father =49

Thank you for this amazing session mam 💖

[kalyaninithya]

3)The father's age is 49 and son's age is 7
Exp:
ATQ,
8(x-1) =
y=
Where x is the age of son and y is that of the father
Putting (2) in (1)

8(x-1) = (x²-1)
8x-8 = x²-1
x²-8x+7

X= 7, 1 (by solving)
One is not possible as the situation is taking about a year before also .
X= 7 years
Y= (7)²= 49 years

[kalyaninithya]

2) POSSIBLE WITH LENGTH= 40 m and BREATH = 20 m
Explanation:
Given : 2(l+b) = 80
lb = 400
L= 400/b
2(400/b+b) = 80
400/b + b = 40 .
400 + b²/b = 40
b²-40b+400 = 0
Splitting the middle term
b²-20b-20b+400= 0
b(b-20) -20(b-20) = 0
(b-20)(b-20) = 0
b= 20
L= 400/20
l= 20 m

[BarkhaGola]

Mam what is the time table for maths class

[rajendarsiripuram]

Let the present age of the son be x.
Let the father's present age be y.
One year ago,  y−1=8(x−1)
⇒y−1=8x−8
⇒y=8x−7
Now applying the condition, we get
(8x−7)=x2
⇒x2−8x+7=0
⇒(x−1)(x−7)=0
⇒x=1 or x=7

Hence, the present age of son is either 1 year or 7 years.

[T_GungunTagore]

• Homework Answer:-
1) The equation becomes kx² - 2kx +6 =0 for the given quadratic equation kx(x-2)+6=0
For having two equal roots, b² - 4ac =0
By solving the value, k is either be 0 or 6 but k =0 is not possible hence the value of k =6
2) The equation would be l² - 40l +400=0 and has two real and equal roots hence, it is possible to design a rectangular park of perimeter 80m and area as 400m² and the Length= 20m and breadth=20m
3) The equation would be x² - 8x +7 =0
By solving the equation x can be 1 or 7 but x² =1 which is not possible as the father's age cannot be equal to the son's age hence, x=7
Therefore, the son's age will be 7 years and the father's age will be 49 years