Polynomials Test

Result

Polynomials Test - 2

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Weekly Quiz Competition

Question 1
1 / -0

If x³ + ax² + bx + 12 leaves remainder 4 when divided by (x - 1), which of the following is the value of a + b?

A
-13

B
-7

C
-5

D
-9

Solution

Let p(x) be x³ + ax² + bx + 12
g(x) = x - 1
On division of p(x) by g(x), remainder = 4
Now, g(x) is linear.
So, g(x) = 0
x - 1 = 0
x = 1
Now, (+1)³ + a (+1)² + b (+1) + 12 = 4
Or, 1 + a + b + 12 = 4
a + b + 13 = 4
a + b = 4 - 13
a + b = -9
Question 2
1 / -0

If the weights of two different quantities are (3x³ - 6x² - 4x + 8) kg and (5x³ - 10x² + 2x - 4) kg, then what is the biggest measure that can weigh both the quantities?

A
(x - 2) kg

B
(x + 2) kg

C
(2x² - 3) kg

D
(5x² + 2) kg

Solution

Weights of two different quantities:
(3x³ - 6x² - 4x + 8) kg and (5x³ - 10x² + 2x - 4) kg

Weight of the first quantity = (3x³ - 6x² - 4x + 8) kg
= 3x²(x - 2) - 4(x - 2)
= (x - 2)(3x² - 4)

Weight of the second quantity = (5x³ - 10x² + 2x - 4) kg
= 5x²(x - 2) + 2(x - 2)
= (x - 2)(5x² + 2)
Therefore, required measure is the H.C.F. of both the weights, i.e (x - 2) kg.
Question 3
1 / -0

The radius and height of a cylindrical pipe are (5x² - 27x) m and (3x² - 20x) m, respectively. Find the surface area of the pipe which is open from both the sides when x = √(49).

A
2450 m²

B
2455 m²

C
2464 m²

D
2472 m²

Solution

Let the radius of the pipe be r and the height be h.

r = (5x² - 27x) m

h = (3x² - 20x) m

When x = √(49)= 7;

r = (5(7)² - 27(7)) m = 245 - 189 = 56 m

h = (3(7)² - 20(7)) m = 147 - 140 = 7 m

Surface area (open cylindrical pipe) = 2πrh

= 2 × 22/7 × 56 × 7 = 2 × 22 × 8 × 7 = 2464 m²