Question

if -2 and a are the zeros of the polynomial x4 -(2a+3)x2-2(a-1)x+12 find a​

Answer 1

HeYa❤️...

Answer:

Given:

-2 and a are the zeroes of polynomial,

$\alpha = - 2 \: and \: \beta = a$

Solution:

[tex] \alpha + \beta = \frac{ - b}{a} \\ - 2 + a = \frac{ - ( - 2(a - 1))}{2a + 3} \\ - 2 + a = \frac{2a - 2}{2a + 3} \\ - 2 + a(2a + 3) = 2a + 3 \\ - 2 + 2a {}^{2} + 3a = 2a + 3 \\ 2a {}^{2} + a = 5 \\ 2a {}^{2} + a = 5.....(i) [/tex]

Product of zeroes = c/a

-2a = 12/2a + 3

-2a (2a + 3) = 12

- 4a^2 - 6a = 12

2a^2 + 3a = -6 .....(ii)

From eq(i) and eq(ii),

a - 3a = 5 + 6

- 2a = 11

a = -11/2

Hence, Value of a is -11/2.

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