Question

find the zero of polynomial and verify the relationship between zeroes and coefficients x^2+x+1​

Answer 1

Answer:

Given quadratic polynomial,

p(x) = 4x² - x - 3

Let's find the zeroes using the splitting the middle term method.

⇒ 4x² - x - 3 = 0

⇒ 4x² - (4 - 3)x - 3 = 0

⇒ 4x² - 4x + 3x - 3 = 0

⇒ 4x(x - 1) + 3(x - 1) = 0

⇒ (x - 1)(4x + 3) = 0

So, x = 1, -3/4

We have found the zeroes, let's verify the relationship between the zeroes and the coefficient.

First : ( Sum of zeroes )

We know,

⇒ Sum of zeroes = -(coefficient of x) / (coefficient of x²)

⇒ 1 + (-3/4) = - (-1) / (4)

⇒ 1 - 3/4 = 1/4

⇒ (4 - 3) / 4 = 1/4

⇒ 1/4 = 1/4

Second : ( Product of zeroes )

As we know,

⇒ Product of zeroes = (constant term) / (coefficient of x²)

⇒ 1 × -3/4 = (-3) / (4)

⇒ -3/4 = -3/4

Hence, Proved!

Step-by-step explanation:

Hope it's helpful to you :) :)

Answer 2

Step-by-step explanation:

• ANSWER IN THE ATTACHMENT..