Question

write the zeroes of the 6xcube-3-7x and verify the relation between zeroes and coefficients ​

Answer 1

Hey!

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Quadratic polynomial - 6x ^2 - 3 - 7x

= 6x^2 - 7x - 3

Splitting the middle term -

6x^2 - 9x + 2x -3

(6x^2 - 9x) + (2x - 3)

3x (2x - 3) + 1 (2x - 3)

(3x + 1) (2x-3)

Zeroes of the polynomial -

3x + 1 = 0

3x = -1

x = -1/3

2x - 3 = 0

2x = 3

x = 3/2

Zeroes are -1/3 and 3/2

Verifying the relationship between the zeroes and the coefficients -:

Sum of zeroes = -1/3 + 3/2 = 7/6

= Coefficient of x / Coefficient of x^2

Product of zeroes = -1/3 × 3/2 = -3/6

= Coefficient of constant /coefficient of x^2

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Hope it helps...!!!