Question

Find the zeros of the quadratic polynomial and verify the relation between zeroes and coefficients 3root3xsquare-19x+10root3
Pls help me!!!
Its very urgent

Answer 1

Answer:

Zeroes are (10 / 3√3) and (√3)

Step-by-step explanation:

Given : f(x) = 3√3x² - 19x + 10√3

By Middle Term Factorisation

→ 3√3x² - 9x - 10x + 10√3

Taking common terms out.

→ 3√3x(x - √3) - 10(x - √3)

→ (3√3x - 10)(x - √3)

To find the zeroes, we use zero product rule.

→ (3√3x - 10) = 0 and (x - √3) = 0

→ x = 10 / 3√3 and x = √3

Let α and β be the zeroes of the above polynomial.

∴ α = 10 / 3√3 & β = √3

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On comparing the above polynomial with ax² + bx + c, we get

a = 3√3, b = - 19, c = 10√3

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Verification:

• Sum of zeroes = α + β

→ (10 / 3√3) + √3

→ [ 10 + √3(3√3) ] / 3√3

→ [ 10 + 9 ] / 3√3

→ 19 / 3√3

Also, Sum of zeroes = - b/a

→ - (- 19) / 3√3

→ 19 / 3√3

• Product of zeroes = αβ

→ (10 / 3√3)(√3)

→ 10/3

Also, Product of zeroes = c/a

→ (10√3) / (3√3)

→ 10/3

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