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Can you find the zeroes of the following polynomial and verify the relationship between the zeros and coefficient 6x^2-3-7x

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6x² - 7x - 3 = 0

⇒ 6x² +2x - 9x - 3 = 0

⇒ 2x(3x+1) - 3(3x+1) = 0

⇒ (3x+1) (2x-3) = 0

⇒ 3x+1 = 0 or 2x - 3 = 0

⇒ 3x = -1 or 2x = 3

⇒ x = -1/3 or x = 3/2

∴ The zeroes are -1/3 and 3/2

Comparing the polynomial with general form ax² + bx +c = 0

Here, a = 6, b = -7 , c = -3

α = -1/3 and β = 3/2

α+β = -b/a

⇒ -1/3 + 3/2 = -(-7)/6

⇒(-2 + 9)/6 = 7/6

⇒ 7/6 = 7/6

αβ = c/a

⇒ -1/3 × 3/2 = -3/6

⇒ -3/6 = -3/6

Verified....