Question

Find the zeroes of 4x² – 5 and verify the relationship between the zeroes and its (±√5/2)
coefficients.​

Answer 1

Answer:

The zeroes of the polynomial are  $\sf x=\dfrac{\sqrt{5}}{2} , -\dfrac{\sqrt{5}}{2}$

Step-by-step explanation:

Given :

polynomial : 4x² - 5

To find :

the zeroes and verify the relationship between zeroes and coefficients

Solution :

Let p(x) = 4x² - 5

To find the zeroes, equate p(x) to 0.

p(x) = 0

4x² - 5 = 0

4x² = 5

x² = 5/4

x = ± √(5/4)

x = ± √5/2

The zeroes of the polynomial are  $\sf x=\dfrac{\sqrt{5}}{2} , -\dfrac{\sqrt{5}}{2}$

Relation between zeroes and coefficients :

For the given polynomial,

• x² coefficient = 4
• x coefficient = 0
• constant term = -5

⇒ Sum of zeroes

=  √5/2 + (-√5/2)

= √5/2 - √5/2

= 0

= 0/4

= -(x coefficient)/x² coefficient

   

⇒ Product of zeroes

= (√5/2) × (-√5/2)

= -5/4

= constant term/x² coefficient

Hence verified!

Answer 2

The zeroes of the polynomial are x = ±√5/2

Step-by-step explanation:

Given :

polynomial : 4x² - 5

To find :

the zeroes and verify the relationship between zeroes and coefficients

Solution :

Let p(x) = 4x² - 5

To find the zeroes, equate p(x) to 0.

p(x) = 0

4x² - 5 = 0

4x² = 5

x² = 5/4

x = ± √(5/4)

x = ± √5/2

The zeroes of the polynomial are x = √5/2 , -√5/2

Relation between zeroes and coefficients :

For the given polynomial,

x² coefficient = 4

x coefficient = 0

constant term = -5

⇒ Sum of zeroes

= √5/2 + (-√5/2)

= √5/2 - √5/2

= 0

= 0/4

= -(x coefficient)/x² coefficient

⇒ Product of zeroes

= (√5/2) × (-√5/2)

= -5/4

= constant term/x² coefficient

Hence verified!