Question

For each of the following, find a quadratic polynomial whose sum and product respectively of
the zeroes are as given. Also find the zeroes of these polynomials by factorisation.
(1)-8/3,4/3 (2) 21/8,5/16 (3) -2√3,-9 (4) -3/2√5,-1/2




with steps completely​

Answer 1

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Find the quadratic polynomial sum and product of whose zeroes are as given also find the zeroes if these polynomial by factorisation. (1) -2√3 ,-9

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EXPLANATION.

Quadratic polynomial whose sum and product are given,

As we know that,

Quadratic Polynomial ⇒ x² - (α + β)x + αβ.

Sum of zeroes of quadratic Equation,

⇒ α + β = -b/a.

⇒ α + β = -2√3.

Product of zeroes of quadratic Equation,

⇒ αβ = c/a.

⇒ αβ = -9.

Put the value in equation, we get.

⇒ x² - (α + β)x + αβ.

⇒ x² - (-2√3)x + (-9).

⇒ x² + 2√3x - 9.

⇒ x² + 2√3x - 9.

As we know that,

⇒ D = b² - 4ac.

⇒ D = (2√3)² - 4(1)(-9).

⇒ D = 12 + 36.

⇒ D = 48.

⇒ D = 4√3.

⇒ x = -b ± √D/2a.

⇒ x = -2√3 ± √4√3/2.

⇒ x = -2√3 - √4√3/3    and   x = -2√3 + √4√3/3.

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Conjugate Roots,

If,

D < 0 ⇒ One Roots = α + iβ  other Roots = α - iβ.

D > 0 ⇒ One Roots = α + √β  other Roots = α - √β.

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