Question

if alpha and beta are zeros of p(x) 5x²+4x-9 then find the value of alpha²-beta²

Answer 1

Hii...☺

Here is your solution...☺

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Since,
$\alpha \: and \: \: \beta \: are \: the \: zeroes \:, we \: have$
⚫. 5x² + 4x -9

=> 5x² + 9x - 5x - 9

=> x ( 5x + 9) - 1 ( 5x + 9)

=> (x - 1) (5x + 9)

$\alpha \: = 1$
and ,

$\beta \: = \: - 9 \div 5$

Now,

${ \alpha }^{2} - { \beta }^{2} \\ = > ( \alpha + \beta )( \alpha - \beta )$
=>[ 1 + (-9/5)] [ 1 - (-9/5)]
=> ( 1 - 9/5) (1 +9/5)
=> ( 5-9/5) ( 5+9/5)
=> -4/5 × 14/5
=> -56/25

Thanks...☺