OP Malhotra Class-11 Quadratic Equations S.Chand ISC Maths Solutions

OP Malhotra Class-11 Quadratic Equations S.Chand ISC Maths Solutions Chapter-10. Step by step Solutions of OP Malhotra S.Chand ISC Class-11 Mathematics with Exe-10 (a), 10 (b), 10 (c), 10 (d), 10 (e), 10 (f) With Chapter Test. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.

OP Malhotra Class-11 Quadratic Equations S.Chand ISC Maths Solutions

Class:	11th
Subject:	Mathematics
Chapter  :	Ch-10 Quadratic Equations of Section -A

Board	ISC
Writer	OP Malhotra
Publications	S.Chand Publications 2020-21

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-: Select Topics :-

Exe-10 (a)

Exe-10 (b)

Exe-10( c)

Exe-10 (d)

Exe-10 (e)

Exe-10 (f)

Chapter Test

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Quadratic Equations OP Malhotra S.Chand ISC Class-11 Maths Solutions

Argand Plane
Any complex number z = x + iy can be represented geometrically by a point (x, y) in a plane, called argand plane or gaussian plane. A purely number x, i.e. (x + 0i) is represented by the point (x, 0) on X-axis. Therefore, X-axis is called real axis. A purely imaginary number iy i.e. (0 + iy) is represented by the point (0, y) on the y-axis. Therefore, the y-axis is called the imaginary axis.

How to Solve Quadratic Equations by Factorization

To solve quadratics by factoring, we use something called “the Zero-Product Property”. This property says something that seems fairly obvious, but only after it’s been pointed out to us; namely:

We can only draw the helpful conclusion about the factors (namely, that one of those factors must have been equal to zero, so we can set the factors equal to zero) if the product itself equals zero. If the product of factors is equal to anything non-zero, then we can not make any claim about the values of the factors.

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Exe-10 (a)

Quadratic Equations OP Malhotra S.Chand ISC Class-11 Maths Solutions

Page 10-3

Find the root of following equations :

Question 1:

2x² + x – 3 = 0

Question 2:

6x² + 7x – 20 = 0

Question 3:

……………….

………………..

………………….

Question 11:

The number of real solution of the equation ……………..

…………….

 

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Exe-10 (b)

Quadratic Equations OP Malhotra S.Chand ISC Maths Solutions

Page 10-5

Solve the following equations :

Question 1:

x⁴ – 5x² + 9 = 0

Question 2:

x⁵ – 242 = 243/x⁵

Question 3:

…………………

………………….

………………….

Question 16:

4^x – 3^x-1/2 =…………..

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Exe-10 (c)

Quadratic Equations OP Malhotra S.Chand ISC Class-11 Maths Solutions

Page 10-10 to 10-11

Question 1:

Without solving, find the nature of the roots of the following equations :

(i)……….

(ii)……….

(iii)……….

(iv)……….

Question 2:

If the equations ……………….

Question 3:

…………………..

…………………..

………………….

Question 29:

The ratio of the roots of the ………………….. parameter α.

Question 30:

If (1-p) is a root of the quadratic …………………… its root are.

……………..

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Exe-10 (d)

Quadratic Equations S.Chand ISC Class-11 Maths Solutions

Page 10-15 to 10-16

Question 1:

Find the condition that one root of ………………………. may be 

(i)……………

(ii)…………….

Question 2:

Find the condition that the ratio between the roots of the ………………….. m :n

Question 3:

……………………

…………………..

……………………

Question 14:

The equation …………………….. real root

………………

………………

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Exe-10 (e)

Quadratic Equations OP Malhotra S.Chand ISC Class-11 Maths Solutions

Page 10-21

Draw the graph of each of the following quadratic function.

Question 1:

y = x² -5x +6 ……

Question 2:

y = -x² + 2x + 3 – 3 ……………..

Question 3:

……………….

…………………….

Question 4:

Solve graphically and campare your answer with …………………….. formula method :

(i)……………….

(ii)……………..

(iii)……………….

(iv)……………..

(v)……………….

(vi)……………..

(vii)……………….

(viii)……………..

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 Exe-10 (f)

OP Malhotra S.Chand ISC Class-11 Maths Solutions

Page 10-28

Question 1:

Show that :

(a)……………….

(b)……………..

(c)……………….

(d)……………..

Question 2:

Explain why ………………….. value of k.

Question 3:

………………….

……………………

………………….

Question 9:

If x be real, prove that ………………….. -5 and 3

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Chapter Test

Quadratic Equations OP Malhotra S.Chand ISC Class-11 Maths Solutions

Page 10-29 to 10-31

Solve the following equation :

Question 1:

5^x+1 + 5^2-x =  5³+ 1

Question 2:

………………….

…………………

…………………….

Question 23:

If α, β are the root of the equation…………………… obtained form ………………..

…………………..

Question 24:

If α, β are the root of ……………………. value of ………….

…………………

 

-: End of Quadratic Equations Solution :-

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