Question

Choose The Correct Answer And Write The Reason

Answer 1

1) we know degree of polynomial never be negative , fractional .
so, option ( A ) and ( B ) both are not polynomial .

2) highest power of any polynomial is known as degree of polynomial so,
here highest power 4
so, degree of polynomial = 4
so, option ( C)

3) a²x = p(x ) = 0
x = 0
so, option ( A ) and ( D )

4) option A reason :- read answer (1)

5) p( 1) = 5(1)² -3(1) + 7
= 5 - 3 + 7 = 12 -3
= 9
option ( B)

6 ) x³ + 1 = (x +1)(x² -x +1)
option ( A )

7) we know
a + b + c = 0
then,
a³ + b³ + c³ = 3abc

so, x³ + y³ + 2³ = 3xy(2) = 6xy
option ( C)

8) P(2) = 2(2)² +3(2) - P = 14 - P = 0
P = 14
option ( D)

9) option ( D) reason :- answer (1)

10 ) ( x + 3)( x -7) = 0
x = -3 and 7
option ( C)

11 ) P(x ) = 2x² - x - 6 divided (x -2)
(x - 2)= 0
x = 2
P(2)
so option ( B)

12) 2(a² + b²) -(a + b)² = 0
2(a² + b²) -a² -b² -2ab = 0
(a - b)² = 0
a = b
so, option ( B)

13) x+ 1 = 0
x = -1 put p(x )
(-1)³ +3(-1)² + 3(-1) +1 = 0
option ( C)

14) (525)² - (475)² =(525+475)(525-475)
= 1000× 50 = 50000,
option is wrong

15) ( a + b) = -1
a³ + b³ -3ab = (a + b)³ -3ab(a + b)-3ab
= (-1)³ -3ab(-1) -3ab = -1 +3ab -3ab = -1
option ( C)

16) use a + b + c = 6
( 2 -a) + (2 - b) + (2 - c) = 0
so,
(2 - a)³ +(2-b)³ + (2 - c)³ -3(2- a)( 2 -b )( 2 -c ) = 0
option ( C)

17 ) a/b + b/a = 1
a² + b² = ab
a² + b² -ab = 0
so,
a³ - b³ = (a - b)(a² + b² -ab) = 0
so , option ( C)

18) x = 1/(2 -√3) = 2 + √3
1/x = 2 - √3
now , x² -4x +1 = x( x -4 + 1/x )
x ( x + 1/x -4 ) = (2 +√3)( 2 +√3 + 2 -√3 -4) = 0
option ( C)

19) option ( D) reason :- answer (2)

20) x +2 = 0 => x = -2
x -2 = 0 => x = 2

a(-2)⁴ +2( -2) -3(-2)² + b(-2) -4 = 0
16a -4 -12 -2b -4 = 0
16a -2b = 20
8a - b = 10 -------(1)

a(2)⁴ +2(2) -3(2)² + b(2) -4 = 0
16a + 4 -12 + 2b -4 = 0
8a + b = 6--------(2)
solve equations (1) anc(2)
a = 1
b = 6

then a + b = 1 + 6 = 7

Answer 2

Hey there!

1) Option (A) and option (B) are not polynomials.
Beacuse thier degree in non positive.

2) Option (C) - 4.
We know that highest power of a polynomial is its degree.

3) Option (A) and Option (D)
a²x = 0
x = 0/a²
x = 0.

4) Option (A)
The remaining has the power in negative.

5) Option (B) - 9

=5x²-3x+7
=5(1)²-3(1)+7
=9

6) x³+1 = (x+1) (x²-x+1)
Option (A)

7) we know that x³+y³+z³=3xyz
x³+y³+2³=3(x)(y)(2) = 6xy
So, option (C)

8) Option (D)
f(2) = 2(2²)+3(2)-p = 8+6-p = 14-p
So, p = 14.

9) Option (D) Not a polynomial.
Beacuse its degree is in non positive.

10) Option (C) -3 and 7.

11) X-2 is a factor. x-2 = 0
x=2.
So, p(2). Option (B)

12) 2(a²+b²) - a²-2ab-b² =0
2a²+2b²-a²-2ab-b²=0
a²+b²-2ab=0
(a-b)²=0
a=b
So, option (B).

13) (x-1) is a factor. so x = 1
-1²+3(-1)²+3(-1)-1
= 1+3-3+1
= 0
So, option (C)

14) It's in the form a²-b²
= a+b(a-b)
=525+475(525-475)
= 1000(50)
= 50000.
There is no option. This is the right answer.

15) a³+b³=(a+b)³-3 ab(a + b).
a³+b³-3ab=(a+b)³-3 ab(a + b)-3ab
=-1²-3ab(-1)-3ab
=-1+3ab-3ab
= -1
So, Option (D)

16) Option (C)
a+b+c=6
2+2+2=6
Substituting in that we get 0.

17) a/b+b/a =1
a²+b²/ab = 1
a²+b²=ab
a²+b²-ab=0
a³-b³=(a-b) ( a²+b²-ab)
= 0
So, Option (D)

18) x= 1/ 2-√3
= 1(2+√3)/2²-√3²
= 2+√3
x²-4x+1 = (2+√3)²-4(2+√3)+1
= 4+3+2(2)(√3)-8-4√3+1
=7+4√3-4√3-7
= 0
Option (C)

19) Option (D)- 3 Zeros.
It's a cubic polynomial,so it has 3 Zeros.

20)
It means 2 and -2 are the zeros.
p(2) ax⁴+2x-3x²+bx-4=0
a2⁴+2(2)-3(2)²+b(2)-4 =0
16a+4-12+2b-4=0
16a+2b=12
2(8a+b)=12
8a+b=6 ----------(1)

p(-2) a(-2)⁴+2(-2)-3(-2)²+b(-2)-4=0
16a-4-12-2b-4=0
16a-2b = 20
8a-b = 10 -------(2)

Solving them we get,
a=1 and b=6

a+b = 1+6=7

:)