Sasi Math (Revised for 1024)

Scroll:Algebra >> Multiple Choice Questions: >> mcq (4180)

Written Instructions:

For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..

For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.

Leave your answers in the simplest form or correct to two decimal places.

If a polynomial p(x) is divided by (ax+b), then the remainder is

1) ab) ' title="p(-

\frac{a}{b}

) "/> p(-

\frac{a}{b}

)
2) ba) ' title="p(-

\frac{b}{a}

) "/> p(-

\frac{b}{a}

)
3) ab) ' title="p(

\frac{a}{b}

) "/> p(

\frac{a}{b}

)
4) ba) ' title=" p(

\frac{b}{a}

) "/> p(

\frac{b}{a}

)

( )

The roots of the polynomial equation x² +2x = 0 are

1) X = 0,2
2) x = 1,-2
3) x =0,-2
4) x = 1,2

( )

The polynomial 3x-2 is a

1) quadratic polynomial
2) linear polynomial
3) cubic polynomial
4) constant polynomial

( )

If the polynomial x³ –ax²+2x-a is divided (x-a), then remainder is

(1)⇒ a

(2)⇒(a²)

(3) ⇒(a³)

(4) ⇒(-a)

1) 2
2) 3
3) 1
4) 4

( )

One of the factors of x³-2x²+2x -1 is

1) x+2
2) x-1
3) x+1
4) x-2

( )

The degree of the polynomial 4x²-7x³+ 6x + 1 is

1) 1
2) 3
3) 2
4) 0

( )

The root of the polynomial equation 3x-1 = 0 is

1) x = 3
2) 13 ' title=" x = -

\frac{1}{3}

"/> x = -

\frac{1}{3}

3) x = 1
4) 13 ' title="x =

\frac{1}{3}

"/> x =

\frac{1}{3}

( )

If ( ax- b) is a factor of p(x), then

1) ba)=0 ' title="p(

\frac{b}{a}

)=0 "/> p(

\frac{b}{a}

)=0
2) p(a)=0
3) ba)=0 ' title="p(-

\frac{b}{a}

)=0 "/> p(-

\frac{b}{a}

)=0
4) p(b)=0

( )

The polynomial 4x²+2x-2 is a

1) quadratic polynomial
2) cubic polynomial
3) constant polynomial
4) linear polynomial

( )

10)

One of the factors of x²- 3x -10 is

1) x-3
2) x-5
3) x+2
4) x-2

( )

If a polynomial p(x) is divided by (ax+b), then the remainder is

1) ba) ' title=" p(

\frac{b}{a}

) "/> p(

\frac{b}{a}

)
2) ab) ' title="p(-

\frac{a}{b}

) "/> p(-

\frac{a}{b}

)
3) ab) ' title="p(

\frac{a}{b}

) "/> p(

\frac{a}{b}

)
4) ba) ' title="p(-

\frac{b}{a}

) "/> p(-

\frac{b}{a}

)

Answer: 4

SOLUTION 1 :

Ans = $\frac{p(-b}{a)}$

The roots of the polynomial equation x² +2x = 0 are

1) x = 1,2
2) x = 1,-2
3) x =0,-2
4) X = 0,2

Answer: 3

SOLUTION 1 :

Hint: [ [x² +2x = 0 ⇒ x(x+2)=0 ⇒ x = 0 (or) x + 2 = 0 ⇒ x=0 (or) x = -2 ⇒ x = 0,-2]

Ans = x = 0, -2

The polynomial 3x-2 is a

1) constant polynomial
2) quadratic polynomial
3) linear polynomial
4) cubic polynomial

Answer: 3

SOLUTION 1 :

Hint: [ The degree of 3x-2 is 1, It is a linear polynomial]

Ans = linear polynomial

If the polynomial x³ –ax²+2x-a is divided (x-a), then remainder is

(1)⇒ a

(2)⇒(a²)

(3) ⇒(a³)

(4) ⇒(-a)

1) 3
2) 2
3) 1
4) 4

Answer: 3

SOLUTION 1 :

Hint:[ [ p(x) = x³ – ax²+ 2x- a ⇒ The zero of x - a is a

p(a) = a³-a(a)²+2(a)-a ⇒ a³ - a³ + 2a - a = 2 ]

Ans = a

One of the factors of x³-2x²+2x -1 is

1) x+2
2) x+1
3) x-2
4) x-1

Answer: 4

SOLUTION 1 :

Hint:[ (x³-2x²+ 2x -1 = x³-x²-x² + x + x -1 = x²(x-1) – x(x-1) + 1(x-1) = (x-1) (x²-x + 1) ]

Ans = x - 1

The degree of the polynomial 4x²-7x³+ 6x + 1 is

1) 1
2) 0
3) 2
4) 3

Answer: 4

SOLUTION 1 :

Hint: [The term having the highest degree is -7x³, The degree is 3]

Ans =3

The root of the polynomial equation 3x-1 = 0 is

1) 13 ' title=" x = -

\frac{1}{3}

"/> x = -

\frac{1}{3}

2) x = 3
3) 13 ' title="x =

\frac{1}{3}

"/> x =

\frac{1}{3}

4) x = 1

Answer: 3

SOLUTION 1 :

Hint: [3x -1 = 0 ⇒ 3x = 1 ⇒ x = $\frac{1}{3}$ ]

Ans = x = $\frac{1}{3}$

If ( ax- b) is a factor of p(x), then

1) p(a)=0
2) ba)=0 ' title="p(

\frac{b}{a}

)=0 "/> p(

\frac{b}{a}

)=0
3) p(b)=0
4) ba)=0 ' title="p(-

\frac{b}{a}

)=0 "/> p(-

\frac{b}{a}

)=0

Answer: 2

SOLUTION 1 :

Hint: [ ax-b is a factor of p(x) ⇒ The zero of ax-b is $\frac{(b}{a)}$ ⇒ p $\frac{(b}{a)}$ =0]

Ans = p $\frac{(b}{a)}$ =0

The polynomial 4x²+2x-2 is a

1) cubic polynomial
2) constant polynomial
3) linear polynomial
4) quadratic polynomial

Answer: 4

SOLUTION 1 :

Hint: [ The degree of 4x²+2x-2 is 2, It is a quadratic polynomial]

Ans = quadratic polynomial

10)

One of the factors of x²- 3x -10 is

1) x+2
2) x-5
3) x-3
4) x-2

Answer: 2

SOLUTION 1 :

Hint : [ x²- 3x -10 = x²-5x + 2x -10 ⇒ x(x-5) + 2(x-5)

The factor of x²-3x -10 are (x-5) and (x+2) ]

Ans = x - 5

Scroll:Algebra >> Multiple Choice Questions: >> mcq (4180)

One of the factors of x3 -2x2 +2x -1 is

One of the factors of x3 -2x2 +2x -1 is

One of the factors of x³-2x²+2x -1 is

One of the factors of x³-2x²+2x -1 is