Question

5. If alpha and Beta are the zeros of the quadratic polynomial p(x) = 4x² - 5x - 1, find the value of
alpha²beta + alphabeta²
?​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Given Quadratic polynomial → 4x² - 5x - 1

To find:

α²β + αβ²

= αβ (α + β)

Solution:

Finding product of zeroes i.e. αβ

$\alpha \times \beta = \dfrac{c}{a}$

$\implies \alpha \beta = \dfrac{ - 1}{4}$

Finding sum of zeroes i.e. α + β

$\alpha + \beta = \dfrac{ - b}{a}$

$\implies \alpha + \beta = \dfrac{ - ( - 5)}{4}$

$\implies \alpha + \beta = \dfrac{5}{4}$

Now,

αβ (α + β)

= -1/4 (5/4)

= -5/16

∴ α²β + αβ² = -5/16

KNOW MORE:

This question can also be solved by factorising the given polynomial and obtaining alpha and beta.