Question

Find the zeores of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. √3y^2+11y+6√3​

Answer 1

Sᴏʟᴜᴛɪᴏɴ :-

→ √3y² + 11y + 6√3 = 0

→ √3y² + 9y + 2y + 6√3 = 0

→ √3y(y + 3√3) + 2(y + 3√3) = 0

→ (y + 3√3)(√3y + 2) = 0

Putting Both Equals to zero now,

→ y = (-3√3)

→ y = (-2)/√3

Hence, Zeros of the given Quadratic Polynomials are (-3√3) & (-2)/√3 ..

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Now, First Relation is :-

→ Sum of Zeros = - (coefficient of x) /(coefficient of x²)

Putting both values ,

→ (-3√3) + (-2)/√3 = -(11)/√3

→ (-3√3*√3 - 2) / √3 = -(11)/√3

→ (-9 - 2) / √3 = -(11)/√3

→ -(11)/√3 = -(11)/√3 1 ✪✪ Hence Verified. ✪✪

Second Relation :-

→ Product Of Zeros = Constant Term / (coefficient of x²)

Putting both Values ,

→ (-3√3) * (-2)/√3 = (6√3)/√3

→ (6√3)/√3 = (6√3)/√3

→ 6 = 6 ✪✪ Hence Verified. ✪✪

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