ব্যাংক ডেইলি কুইজ [লং কোর্সের অংশ]

Question: The roots of the quadratic equation 6x² - x - 2 = o are -

Solution:
6x² - x - 2 = o
⇒ 6x² - 4x + 3x - 2 = o
⇒ 2x(3x - 2) + 1 (3x - 2) = o
⇒ (2x + 1)(3x - 2) = 0

So, 2x + 1 = 0
x = - 1/2

Or, 3x - 2 = 0
x = 2/3 

Question: The solution of 2x² + 3x - 2 = 0 are

Solutiuon:
Given,
2x² + 3x - 2 = 0
⇒ 2x² + 4x - x - 2 = 0
⇒ 2x(x + 2) - 1(x + 2) = 0
⇒ (x + 2) (2x - 1) = 0

So, x + 2 = 0
x = - 2

Or, 2x - 1 = 0
∴ x = 1/2

Question: The value of the polynomial 5x³ - 4x² + 3 when x = - 1 is

Solution:
5x³ - 4x² + 3
If x = - 1,
then replace x with - 1,

We get,
5x³ - 4x² + 3 = 5 × (- 1)³ - 4(- 1)² + 3
= - 5 - 4 + 3
= - 6

Question: The product of two consecutive positive integers is 360. To find the integers, this can be represented in the form of a quadratic equation as- 

Solution:
Let x and (x + 1) be the two consecutive integers.

According to the given,
x(x + 1) = 360
⇒ x² + x = 360
⇒x² + x - 360 = 0
⇒x² + 18x - 17x - 360 = 0
⇒(x +18)(x - 17) = 0
x ≠ - 18,
∴ x = 17

One positive interger 17.
Other positive interger 17 + 1 = 18.

x² + x - 360 = 0 is the required quardratic equation. 

Question: What is the sum of the reciprocals of the values of zeroes of the polynomial 6x² + 3x² - 5x + 1?

Solution: 
6x² + 3x² - 5x + 1
⇒ 9x² - 5x + 1
Let α and β are two roots of the equations

As we know,
Sum of roots (α + β) = 5/9
Product of roots (αβ) = 1/9

ATQ,
1/α + 1/β = (α + β)/αβ
= (5/9)/(1/9)
= (5/9) × (9/1)
= 5