Find the zeroes of the polynomial f(x)= 2x² - 5x + 3 and verify the relationship between the zeroes and the coefficients.

The polynomial

f(x) =2ˣ² - 5x + 3

zeroes of the polynomial f(x)= 2x² - 5x + 3

By factorizing we have ,

→ 2x² - 5x + 3

→2x² -2x - 3x + 3

→2x(x-1)-3(x-1)

→(2x-3)(x-1)

Now the zeroes are

→ 2x - 3 = 0 and → x - 1 = 0

→ x = 3/2 and → x = 1

Verification of relation

Sum of the zeroes = -b/a

⇒ 3/2 + 1 = -(-5/2)

⇒ (3+2)/2 = 5/2

⇒ 5/2 = 5/2

Product of the zeroes = c/a

⇒ 3/2×1 = 3/2

⇒ 3/2 = 3/2

Verified

I hope it will help you.

Regards.

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