Question

If alpha beta are zeroes pf quadratic polynomial x2-6x+a , find th e vaue of a if 3alpha+2 beta =20

Answer 1

we know that ,sum of zeroes=

$\alpha + \beta = \frac{ - b}{a} = \frac{6}{1} = 6$
__________________________(1)
also , product of zeroes,

$\alpha \beta = \frac{c}{a} = a$
________________________(2)

now...

$3 \alpha + 2 \beta = 20$
_________________________(3)

multiply 2 to (1) and subtract (1) from (3),

$3 \alpha + 2 \beta = 20 \\ 2\alpha + 2 \beta = \: 12\\......................... \\ \alpha = 8 \\ ............................$
from (1),


$\beta = 6 - 8 = - 2$
from (3),

$\alpha \beta = a \\ \\ a = 8 \times - 2 \\ = - 16$

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Answer 2

Your answer is here ......