Question

Find the zeroes of polynomial 5x² - 4x-12 and also verify the relationship between zeroes and coefficients of polynomials.​

Answer 1

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Answer 2

Given :-

5x² - 4x - 12

To Find :-

Zeroes

Solution :-

Spilt middle term

5x² - 4x - 12

5x² - (6x - 10x) - 12

5x² - 6x + 10x - 12

x(5x + 6) - 2(5x + 6)

(5x + 6)(x - 2)

Either

5x + 6 = 0

5x = -6

x = -6/5

or,

x - 2 = 0

x = 2

Verification

Sum of zeroes = -b/a

-6/5 + 2 = -(-4)/5

-6 + 10/5 = 4/5

4/5 = 4/5

Product of zeroes = c/a

-6/5 × 2 = -12/5

-12/5 = -12/5