Question

Form a quadratic equations when sum of zeroes is -6 and product of zeroes is -4

Answer 1

EXPLANATION.

Quadratic equation.

Sum of the zeroes = - 6.

Products of the zeroes = - 4.

As we know that,

Sum of the zeroes of the quadratic equation.

⇒ α + β = -b/a.

⇒ α + β = - 6. - - - - - (1).

Products of the zeroes of the quadratic equation.

⇒ αβ = c/a.

⇒ αβ = - 4. - - - - - (2).

As we know that,

Formula of quadratic polynomial.

⇒ x² - (α + β)x + αβ.

Put the value in this equation, we get.

⇒ x² - (-6)x + (-4) = 0.

⇒ x² + 6x - 4 = 0.

                                                                                                                     

MORE INFORMATION.

Conjugate roots.

(1) = If D < 0.

One roots = α + iβ.

Other roots = α - iβ.

(2) = If D > 0.

One roots = α + √β.

Other roots = α - √β.

Answer 2

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EXPLANATION.

Quadratic equation.

Sum of the zeroes = - 6.

Products of the zeroes = - 4.

As we know that,

Sum of the zeroes of the quadratic equation.

⇒ α + β = -b/a.

⇒ α + β = - 6. - - - - - (1).

Products of the zeroes of the quadratic equation.

⇒ αβ = c/a.

⇒ αβ = - 4. - - - - - (2).

As we know that,

Formula of quadratic polynomial.

⇒ x² - (α + β)x + αβ.

Put the value in this equation, we get.

⇒ x² - (-6)x + (-4) = 0.

⇒ x² + 6x - 4 = 0.

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