Question

If α and β are the zeroes of the quadratic
polynomial p(x) = 4x² - 5x + 1, then find
the value of α2β+β2α.​

Answer 1

Answer:

∝²β + β²∝ = $\dfrac{5}{16}$

Step-by-step explanation:

We have been given the equation:-

4x² - 5x + 1

It has two roots ∝ and β

And were are required to find the value of:-

∝²β + β²∝

We can re-write is as:-

∝β(∝+β)

It is nothing but Products of Roots multiplied by Sum of Roots.

It's value would be:-

= $\dfrac{c}{a} \times \dfrac{-b}{a}$

= $\dfrac{1}{4} \times \dfrac{-(-5)}{4}$

= $\dfrac{1}{4} \times \dfrac{5}{4}$

= $\dfrac{5}{16}$

So, the value of ∝²β + β²∝ is $\dfrac{5}{16}$

Answer 2

What is a polynomial?

A polynomial is an algebraic expression having the degree of it's variables as a whole number.

For example - 2, x , x+4, 4x³ etc.

The classification of polynomials can be done in two ways :

• On the basis of degree :

★ Linear Polynomial - The polynomial having the degree = 1

★ Quadratic Polynomial - The polynomial having the degree = 2

★ Cubic Polynomial - The polynomial having the degree = 3

• On the basis of terms :

★Monomial : The polynomial having a single term only.

★ Binomial : The polynomial having two terms.

★ Trinomial : The polynomial having 3 terms.