Question

If α, β are the zeroes of the polynomial x² – 16, then αβ(α + β) is​

Answer 1

Answer:

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Step-by-step explanation:

$\alpha + \beta = 0 \\ \alpha \beta = - 16 \\ \\ \alpha \beta ( \alpha + \beta ) = - 16 \times 0 \\ \\ = 0$

Answer 2

Topic

Quadratic Equation

To Find

$\alpha \beta(\alpha + \beta)$

Given

$\alpha,\beta$ are the zeroes of the polynomial x² - 16.

Solution

x² - 16 = 0

Add 16 to both sides,

x² = 16

Take Square root in both sides,

x = 4 or -4

So,

$\alpha \:and\: \beta$ are 4 and -4 respectively.

$\alpha\beta= -16$

$\alpha + \beta = 0$

Now, put the values in equation,

$\alpha \beta(\alpha + \beta)$

-16( 0 )

Any integer multiplied with '0' becomes '0'.

So,

-16( 0 ) = 0

Answer

$So,\:\alpha \beta(\alpha + \beta)=0$

Information:-

Zeroes of the polynomial

Zeroes of the polynomial are the numbers at which given polynomial becomes zero.