Question

$if \: \alpha \: and \: \beta \: are \: the \: zeroes \: of \: p(x) = {x}^{2} - 5x + 6 \: then \: value \: of \: \alpha + \beta - 3 \alpha \beta \: is$
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Answer 1

$\bigstar$ Question :

If α and β are the zeroes of p(x) = x²-5x+6.Then find the value of

α+β-3αβ

$\bigstar$ Solution :

Compare given equation with ax²+bx+c , we get ,

a = 1 , b = - 5 , c = 6

Now , sum of zeroes , α+β = -b/a

=> α+β = -(-5)/1=5

=> α+β = 5 ...(1)

Product of zeroes , αβ = c/a = 6/1

=> αβ = 6 ...(2)

Now the value of α+β-3αβ is ,

α+β-3αβ

=> 5 - 3(6) [ From (1) & (2) ]

=> 5 - 18

=> - 13

                                                 

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Answer 2

✰✰ ANSWER ✰✰

$\longrightarrow{{x}^{2}+5x+6}$

Comparing with ax²+bx+c : -

• a = 1
• b= 5
• c= 6

$\longrightarrow{Sum\:of\:Zeroes=\dfrac{-b}{a}}$

$\longrightarrow{\alpha+beta=\dfrac{-5}{1}}$

$\longrightarrow{\alpha+\beta=-5}$

$\longrightarrow{Product\:of\:Zeroes=\dfrac{c}{a}}$

$\longrightarrow{\alpha\beta=\dfrac{6}{1}}$

$\longrightarrow{\alpha\beta=6}$

Now,Put values in α+β=3αβ : -

$\longrightarrow{\alpha+\beta-3\alpha\beta}$

$\longrightarrow{-5-3(6)}$

$\longrightarrow{-5-18}$

$\longrightarrow{\textbf{-13}}$