Question

If α, β are zeroes of x² –6x + k, what is the value of k if 3α + 2β = 20?

–16

8

16

None of These

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Answer 1

Answer:

K= -16

Step-by-step explanation:

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Answer 2

Answer:

k = (-16)

Step-by-step explanation:

Since they are the zeroes of polynomial

So,

$\alpha + \beta = \frac{ - b}{a}$

$\alpha \beta = \frac{c}{a}$

Putting value of a and b from equation.

$\alpha + \beta = \frac{ -( - 6) }{1}$

$\alpha + \beta = 6..............(1)$

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

Multiply equation (1) by 3

$3 \alpha + 3 \beta = 18$

Subtract them.

$3 \beta - 2 \beta = 18 - 20$

$\beta = ( - 2)$

Put Beta value in equation (1) we get

ALPHA + (-2) = 6

alpha - 2 = 6

Alpha = 8

Now,

we know

Product of zeroes = c/a

So,

$\alpha \beta = \frac{c}{a}$

(8) X (-2) = k/a

-16 = k/1

k = (-16)

HOPE IT HELPS YOU