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A point both of whose coordinates are negative will lie in A. I quadrant B. II quadrant C. III quadrant D. IV quadrant

The correct answer is C. III quadrant Solution 3rd Quadrant: The lower left-hand corner of the graph is the third quadrant. It contains... View Article

The point at which the two coordinate axes meet is called the A. abscissa B. ordinate C. origin D. quadrant

The correct answer is C. origin Solution Origin: The coordinate axes intersect each other at right angles, The point of intersection of these... View Article

Ordinate of all points on the x-axis is A. 0 B. 1 C. – 1 D. any number

The correct answer is A. 0 Solution The abscissa and ordinate are used to represent the position of a point on a graph. The coordinates of the... View Article

Abscissa of all the points on the x-axis is (A) 0 (B) 1 (C) 2 (D) any number

Answer: (D) any number The abscissa of all the points on the x-axis can be any number. The abscissa and ordinate are used to represent the... View Article

Point (- 10, 0) lies A. on the negative direction of the x-axis B. on the negative direction of the y-axis C. in the third quadrant D. in the fourth quadrant

The correct answer is A. on the negative direction of the x-axis Solution The abscissa and ordinate are used to represent the position of a... View Article

Point (0, -7) lies A. on the x -axis B. in the second quadrant C. on the y-axis D. in the fourth quadrant

The correct answer is C. on the y-axis SolutionThe coordinates of the X-axis on the cartesian plane is called abscissa. It is the distance... View Article

Signs of the abscissa and ordinate of a point in the second quadrant are respectively A. + , + B. -, – C. -, + D. + , –

The correct answer is C. –, + Solution In Quadrant 2 Co-ordinate Plane the points are in the form: (-x, +y) (-3,5) is of form (-x,y).... View Article

Point (-3, 5) lies in the A. first quadrant B. second quadrant C. third quadrant D. fourth quadrant

The correct answer is B. second quadrant Solution In Quadrant 2 Co-ordinate Plane the points are in the form: (-x, +y) (-3,5) is of form... View Article

Without actual division, prove that 2x⁴ – 5x³ + 2x² – x + 2 is divisible by x² – 3x + 2. [Hint: Factorise x² – 3x + 2]

Given f(x) = 2x4 – 5x3 + 2x2 – x + 2 To Prove 2x4 – 5x3 + 2x2 – x + 2 is divisible... View Article

If both x – 2 and x – 1/2 are factors of px² + 5x + r, show that p = r.

Given f(x) = px2+5x+r and factors are x-2, x – 1/2 To Prove We have to prove that p = r.. Proof f(x) = px2+5x+r and... View Article

The polynomial p(x) = x⁴ – 2x³ + 3x² – ax + 3a – 7 when divided by x + 1 leaves the remainder 19. Find the values of a. Also find the remainder when p(x) is divided by x + 2.

Given p(x) = x4 – 2x3 + 3x2 – ax + 3a – 7 when divided by x + 1 leaves the... View Article

If the polynomials az³ + 4z² + 3z – 4 and z³ – 4z + a leave the same remainder when divided by z – 3, find the value of a.

Given p(z)=az3 + 4z2 + 3z – 4 p1(z)= z3 – 4z + a on dividing by z – 3 leave the same reminder Find... View Article

If + 2 is a factor of ⁵ – 4 2 ³ + 2 + 2 + 3, find a.

Solution According to the given details Let p(x) = x5 – 4a2x3 + 2x + 2a + 3 g(x) = x + 2a g(x) = 0... View Article

For what value of m is ³ – 2 ² + 16 divisible by x + 2?

Solution According to the given details Let p(x) = x 3 – 2mx2 + 16, g(x) = x + 2 g(x) = 0 ⟹ x + 2... View Article

Show that p – 1 is a factor of p¹⁰ – 1 and also of p¹¹ – 1.

Solution Let f(p) = 10 − 1,and m(p) = – 1 zero of m(p) ⇒ m(p) = 0 p – 1 = 0 p = 1... View Article

Determine which of the following polynomials has x – 2 a factor: (i) 3 ² + 6 −24. (ii) 4 ² + −2.

Solution (i) 3 2 + 6 −24. Let p(x) =3 2 + 6 −24 g(x) = x – 2 g(x) = x – 2 zero of g(x) ⇒ g(x) =... View Article

Show that: (i) + 3 is a factor of 69 + 11 − ² + ³. (ii) 2 −3 is a factor of + 2 ³ – 9 ² + 12

Solution (i) + 3 is a factor of 69 + 11 − 2 + 3. Let us assume that p(x) = 69 + 11x −... View Article

Check whether p( ) is a multiple of g( ) or not: (i) p( ) = ³ – 5 ² + 4 – 3, g( ) = – 2 (ii) p( ) = 2 ³ – 11 ²− 4 + 5, ( ) = 2 + 1

Solution (i) p( ) = 3 – 5 2 + 4 – 3, g( ) = – 2 According to the given details g(x)=x –... View Article

By Remainder Theorem find the remainder, when p(x) is divided by g(x), where (i) p( ) = ³ – 2 ² – 4 – 1, g( ) = + 1 (ii) p( ) = ³ – 3 ² + 4 + 50, g( ) = – 3 (iii) p( ) = 4 ²³ – 12 ² + 14 – 3, g( ) = 2 – 1 (iv) p( ) = ³ – 6 ² + 2 – 4, g( ) = 1 – 3/2

Solution The remainder theorem says that if a polynomial p(x) is divided by a linear factor (x-a) then the remainder is obtained as p (a) (i)... View Article

By actual division, find the quotient and the remainder when the first polynomial is divided by the second polynomial: x⁴ + 1; x -1

Solution On performing the long division method to the given polynomial x4 + 1 by x-1 we obtain Hence, Quotient = x3 +... View Article

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