Question

Which one of the following is not a quadratic equation?
(1) (x + 1)2 = 4(x + 5)
(2) x2 + 2x = (7 - 3x)2
n (3) (x+3)(x + 1) = x2 - 4x + 5
(4) x - x2 + x + 2 = (x + 2
n oint of (43) and (-2.7) is
A​

Answer 1

Answer:

Step-by-step explanation:

Solution:

 

(i) x³+x²+x+1

 

Let p(x)= x³+x²+x+1

 

 

The zero of x+1 is -1.

 

On putting x= -1

p(−1)=(−1)³+(−1)²+(−1)+1

=−1+1−1+1=0

Hence, by factor theorem, x+1 is a factor of x³+x²+x+1

 

(ii) x4 + x3 + x2 + x + 1

 

Let p(x)= x⁴+x³+x²+x+1

 

The zero of x+1 is -1.

 

On putting x= -1

p(−1)=(−1)⁴+(−1)³+(−1)²+(−1)+1

 

=1−1+1−1+1=1≠0

 

Hence, by factor theorem, x+1 is not  a factor

of x⁴+x³+x²+x+1

 

 (iii) x4 + 3x3 + 3x2 + x + 1 

 

Let p(x)= x⁴+3x³+3x²+x+1

 

The zero of x+1 is -1.

 

On putting x= -1

p(−1)=(−1)⁴+3(−1)³+3(−1)²+(−1)+1

 

=1−3+3−1+1

=1≠0

 

Hence,by factor theorem, x+1 is not a factor of x⁴+3x³+3x²+x+1

 

(iv) x³–x²–(2+√2)x+√2

 

Let p(x)= x³–x²–(2+√2)x+√2

 

The zero of x+1 is -1.

On Putting x= -1

p(−1)=(−1)³–(−1)²–(2+√2)(−1)+√2

Hence, by factor theorem, x+1 is not a factor of x³–x²–(2+√2)x+√2.

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Answer 2

if u get x² (x not equal 0) that will be