Question

7.
Find the zeroes of the quadratic polynomial 6x² - 2x - 8 and verify the
relationship between the zeroes and the co-efficients.​

Answer 1

Step-by-step explanation:

Given :

p(x) = 6x² - 2x - 8

To find :

Relationship between the zeroes and the coefficients.

Solution :

We have,

=> 6x² - 2x - 8

Factorizing we get,

=> 6x² - 2x - 8 [Divide whole equation with 2]

=> 3x² - x - 4

=> 3x² - 4x + 3x - 4

=> 3x² + 3x - 4x - 4

=> 3x(x + 1) - 4(x + 1)

=> (3x - 4) = 0 & (x + 1) = 0

=> 3x = 4 & x = -1

=> x = 4/3 & x = -1

Sum of zeroes,

=> (α+β) = -b/a

=> (4/3 +(-1)) = -(-1/3)

=> (4/3 - 1) = 1/3

=> 1/3 = 1/3

∴ L.H.S = R.H.S

Product of zeros,

=> (αβ) = c/a

=> (4/3 × - 1) = -4/3

=> -4/3 = -4/3

∴ L.H.S = R.H.S

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