Question

kindly solve this step by step with explanation, ... pls i will give more points and mark u as brainliest ​

Answer 1

Answer:

(1) - Option (3)

(2) - Option (2)

Step-by-step explanation:

(i)

Given Equation is f(t) = t² - 5t + 3

Here, a = 1, b = -5, c = 3

α,β are the zeroes of the polynomial.

(i) Sum of zeroes:

α + β = -b/a

α + β = 5

(ii) Product of zeroes:

αβ = c/a

αβ = 3

Now,

α⁴β³ + α³β⁴

= α³β³(α + β)

= (αβ)³(α + β)

= (3)³(5)

= 27 * 5

= 135

(2)

Given Equation is f(x) = x² + 7x + 3

Here, a = 1, b = -7, c = 3

α,β are the zeroes of the polynomial.

(i) Sum of zeroes:

α + β = -b/a

α + β = -7

(ii) Product of zeroes:

αβ = c/a

αβ = 3

Now,

(α - β)² = (α + β)² - 4αβ

           = (-7)² - 4(3)

           = 49 - 12

         = 37

Hope it helps!

Answer 2

Given Equation is f(x) = x² + 7x + 3

Here, a = 1, b = -7, c = 3

α,β are the zeroes of the polynomial.

(i) Sum of zeroes:

α + β = -b/a

α + β = -7

(ii) Product of zeroes:

αβ = c/a

αβ = 3

Now,

(α - β)² = (α + β)² - 4αβ

           = (-7)² - 4(3)

           = 49 - 12

         = 37