Question

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

α² β + αβ².​

Answer 1

Answer:

The value of α²β + αβ² is –5/16.

Step-by-step explanation:

Given polynomial = 4x² – 5x – 1

In the polynomial =

• a = 4
• b = –5
• c = –1

★ Sum of zeros :

$\longrightarrow$ α + β = –b/a

$\longrightarrow$ –(–5)/4

$\longrightarrow$ 5/4 ------ (I)

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★ Product of zeros :

$\longrightarrow$ αβ = c/a

$\longrightarrow$ –1/4 ------ (II)

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★ Value of α²β + αβ² :

$\longrightarrow$ αβ(α + β)

$\longrightarrow$ (–1/4) × (5/4) ------ (substitute I and II)

$\longrightarrow$ –5/16

Therefore, the value of α²β + αβ² is –5/16.

Answer 2

Answer:

Question :-

• If α and β are the zeroes of the quadratic polynomial p(x) = 4x² - 5x - 1, find the value of α²β + αβ².

Given :-

• If α and β are the zeroes of the quadratic polynomial p(x) = 4x² - 5x - 1.

Find Out :-

• The value of α²β + αβ².

Solution :-

p(x) = 4x² - 5x - 1

➻ a = 4

➻ b = - 5

➻ c = - 1

We, know that

Sum of roots = $\dfrac {-b}{a}$

Sum of roots = $\dfrac {(-)(-5)}{4}$

Sum of roots = $\dfrac{5}{4}$

We, know that

Product of the roots = $\dfrac{c}{a}$

Product of the roots = $\dfrac{- 1}{4}$

We have to find the value of the α²β + αβ²

$\Rightarrow$ (αβ) (α +β)

$\Rightarrow$ $\dfrac{- 1}{4} \times\dfrac{5}{4}$

$\Rightarrow$ $\dfrac{- 5}{16}$

$\therefore The\: value\: of\: α^2β + αβ^ 2\: is\: \dfrac{- 5}{16}$