Question

find the zeroes of the following polynomial
by factorisation method and verify the
relaction between the zeress and the
coefficient of the Polynomial.
4×2-3×-1​

Answer 1

Answer:

The polynomial is 4x² - 3x - 1

a + b = -3

a × b = 4 × -1 = -4

1 + -4 = -3

1 × -4 = -4

4x² - 3x - 1 = 0

4x² - 4x + x - 1 = 0

4x(x - 1) + 1(x - 1) = 0

(x - 1)(4x + 1) = 0

x - 1 = 0 4x + 1 = 0

x = 1 4x = -1

x = -1/4

Let alpha = 1 and beta = -1/4

alpha + beta = 1 - 1/4 = 4/4-1/4 = 3/4

-b/a = -(-3)/4 = 3/4

i. e., alpha + beta = -b/a

alpha × beta = 1 × - 1/4 = -1/4

c/a = -1/4

i. e., alpha × beta = c/a

Hence the relationship is verified.

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