Quadratic Equations: Solution of Quadratic Equations | CBSE MATH | Class 10 | Chapter 4 | Lesson 1

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[rajkumar-ukjn]

h.w
q1
(i) Given, x2 – 3x – 10 =0

Taking LHS,

=>x2 – 5x + 2x – 10

=>x(x – 5) + 2(x – 5)

=>(x – 5)(x + 2)

The roots of this equation, x2 – 3x – 10 = 0 are the values of x for which (x – 5)(x + 2) = 0

Therefore, x – 5 = 0 or x + 2 = 0

=> x = 5 or x = -2
(ii)Given, 100x2 – 20x + 1=0

Taking LHS,

= 100x2 – 10x – 10x + 1

= 10x(10x – 1) -1(10x – 1)

= (10x – 1)2

The roots of this equation, 100x2 – 20x + 1=0, are the values of x for which (10x – 1)2= 0

∴ (10x – 1) = 0 or (10x – 1) = 0

⇒x = 1/10 or x = 1/10
q2
Let us say, the base of the right triangle is x cm.

Given, the altitude of right triangle = (x – 7) cm

From Pythagoras theorem, we know,

Base2 + Altitude2 = Hypotenuse2

∴ x2 + (x – 7)2 = 132

⇒ x2 + x2 + 49 – 14x = 169

⇒ 2x2 – 14x – 120 = 0

⇒ x2 – 7x – 60 = 0

⇒ x2 – 12x + 5x – 60 = 0

⇒ x(x – 12) + 5(x – 12) = 0

⇒ (x – 12)(x + 5) = 0

Thus, either x – 12 = 0 or x + 5 = 0,

⇒ x = 12 or x = – 5

Since sides cannot be negative, x can only be 12.

Therefore, the base of the given triangle is 12 cm and the altitude of this triangle will be (12 – 7) cm = 5 cm.
thank mammm my name is kanishita

[T_GungunTagore]

• Homework Answer:-
1) Number of articles will be 6 and the cost of each article will be Rs.15
2) Equation will be 2x² - 14x -120 =0 or x² -7x -60 =0
By solving the equation - The other two sides of a triangle are 5cm and 12cm
3) Roots of the equation x² - 3x -10 =0 will be (5, -2)
(ii) Roots of the equation 100x² -20x +1 =0 will be (1/10, 1/10)
Thankyou ma'am for this session 😄🌟

[umakannan]

please teach trignometry please
1 By Pythagoras theorem,
Side a=12cm and b=5cm
2. x=-2, 5


3. solving 100x²-20x+1=0
x=1/10, x=1/10

[HarleenKaur-hhbf]

Homework Question:-
1) number if articles per day will be 6 and cost of each articles will be Rs. 15
2) Equation would be 2x²-14x-120=0
It can be simplified as x²-7x-60=0
By solving it the base will be 12 cm and altitude will be 5 cm.
3) i) (5, -2)
ii) (1/10, 1/10)

Thankyou so much mam for this wonderful amazing awesome session 😊😊
Mam, we would like if you do a session on the derivation of quadratic formula please mam 😊

[AishaMaster-]

😊THANK YOU MAM for the fabulous explaining ☺️☺️☺️☺️☺️🥰
Homework question:- last question's Answer
x=6, -15/2
Q1) Let.
The base of the right angle triangle be x. And the altitude is x- 7.
My Pythagoras is theeuram equation we got.,
》2x²-14x-120
By MIDDLE TERM SPLITING,
X=12, -12
But base can't be in negative, so taking the positive number.
Base =12cm
Altitude =12-7
= 5cm.
Q2)i] by Apply middle term splitting.,
X= -2, 5
ii] by Apply middle term splitting.,
X=1/10

[nirbhaysingh]

Homework questions :- 2x²+3x-90=0
2x²-12x+15x-90=0
2x(x-6)15(x-6)
x=-15/2, x=6 since the no of articles cannot be negative so x=6 are the no. Of articals
Now 3+2x =3+12=15 therefore cost will be 15

1. Base is 12cm and amplitude is 5cm

3) (i) 5, -2
(ii)0.1, 0.1

[shrutipriya]

Q1. 1
Q2. 0 and -2
Q3. -2, 3/2
Q4 -root2, -5/root2
Q5 1/4square

[kanak]

Homework Q

1) which was last Q
No.of article is 6 and cost is 15 rupees

Last slide
1) base is 12cm and altitude is 5cm

2) i) 5, -2
ii) 1/10, 1/10


Thankyou ma'am for this wonderful session ✨

[SUNIL-rlyt]

Let
x
be the base of the triangle, then the altitude will be
(
x
−
7
)
.

By Pythagoras theorem,

x
2
+
(
x
−
7
)
2
=
(
13
)
2

2
x
2
−
14
x
+
49
−
169
=
0

2
x
2
−
14
x
−
120
=
0

x
2
−
7
x
−
60
=
0

x
2
−
12
x
+
5
x
−
60
=
0

(
x
−
12
)
(
x
+
5
)
=
0

x
=
12
,
x
=
−
5

Since the side of the triangle cannot be negative, so the base of the triangle is
12
c
m
and the altitude of the triangle will be
12
−
7
=
5
c
m
.

[Aqsa_]

🔵HOMEWORK QUESTIONS🔵
53:57

1) Let the base of the triangle be x
So, the altitude will be x-7
Given : Hypotenuse is 13cm
Using PYTHAGORAS THEOREM,
H²= P² + B²
13²=x² +(x-7)²
120= 2x²-14x {taking 2 common}
x²-7x-60=0
x -12x+5x-60=0
x=12 ; x=-5
As length can't be negative, so taking x= 12
Base of triangle = 12cm
Altitude of triangle = 12-7= 5cm


2) Finding roots of:-

a} x²-3x -10=0
x²-5x+2x-10=0
x(x-5) +2(x-5) = 0
x= 5 ; x= -2

b) 100x²-20x+1=0
100x²-10x-10x+1=0
10x(10x-1) -1(10x-1) =0
(10x-1) (10x-1) = 0
x= 1/10 ; x=1/10

53:28 Answer
Number of articles = 6
Cost of each article = Rs 15

[DivishaJayashree]

Good evening mam
Today's homework questions answers:-
Ques1.) By Pythagoras theorem,
Side a=12cm and b=5cm
Ques.2) solving x²-3x-10=0; x=-2, x=5
Ques.3) solving 100x²-20x+1=0
x=1/10, x=1/10
Thank you mam for amazing session..😊😊

[Mahek]

Homework question:-
Number of articles per day will be 6 and the cost of each article will be 15 rupees
1)12 cm and 5 cm
2)i) x=-2, 5
ii)x=1/10, 1/10

Thank you for this amazing session mam 💖

[divyanshigaur]

Ma'am some questions are left from this exercise ... whatt about themm 😢🙂....
Ma'am Youu r myy favv ...When u will teach, it will be understand by me very very easily please make a session for these questions too ...
We want justice for those questions 😅❤....
But the session was good apart from thiss....😊❤

[Nithya-uqrb]

Ans.1 5 cm and 12 cm
Ans.2 i)-2, 5
ii)1/10, 1/10
Thank you mam for explaining clearly ☺️

[BarkhaGola]

Good evening mam i am dhwani homework question 1) b=12cm a=5cm 2) a) x=5, x=-2 b) x=1/10, 1/10

[AnshuKashyap]

We’ve noticed that there haven’t been any new video uploads for over a week. We are very excited about the chapters and eager to resume the remaining content. Please take this matter seriously and let us know when we can expect new uploads. We really appreciate your hard work and look forward to the next installment!😢

[vaidehidekate]

📚Home work Answer:-
A.1. 5cm and 12cm
A.2. i)-2, 5
ii) 1/10, 1/10
Thanks for the amazing session

[Singingdancing__lover]

Good evening mam I'm sreeja
Home work answers
1) 12cm, 5cm
2) a) x=5, x=-2
b) x=-1/10 x= -1/10 😢😢

[blackpinkandbts]

Mam my exam started on 24th of this month so can plz upload this chpter mcq

[shrutipriya]

Hw ans Q1 12, 5
Q2 i)-2, 5
Q2 ii) 1/10, 1/10