Question

write the quadratic polynomial is whose Sum of zeroes is -3/2 and product of zeroes is -1​

Answer 1

EXPLANATION.

Quadratic polynomial.

Sum of the zeroes = -3/2.

Products of the zeroes = -1.

As we know that,

Sum of the zeroes of the quadratic equation.

⇒ α + β = -b/a.

⇒ α + β = -3/2.

Products of the zeroes of the quadratic equation.

⇒ αβ = c/a.

⇒ αβ = -1.

As we know that,

Formula of quadratic polynomial.

⇒ x² - (α + β)x + αβ.

Put the values in the equation, we get.

⇒ x² - (-3/2)x + (-1) = 0.

⇒ x² + 3x/2 - 1 = 0.

⇒ 2x² + 3x - 2 = 0.

                                                                                                                     

MORE INFORMATION.

Nature of the roots of the quadratic expression.

(1) = Real and unequal, if b² - 4ac > 0.

(2) = Rational and unequal, if b² - 4ac is a perfect square.

(3) = Real and equal, if b² - 4ac = 0.

(4) = If D < 0 Roots are imaginary and unequal Or complex conjugate.

Answer 2

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EXPLANATION.

Quadratic polynomial.

Sum of the zeroes = -3/2.

Products of the zeroes = -1.

As we know that,

Sum of the zeroes of the quadratic equation.

⇒ α + β = -b/a.

⇒ α + β = -3/2.

Products of the zeroes of the quadratic equation.

⇒ αβ = c/a.

⇒ αβ = -1.

As we know that,

Formula of quadratic polynomial.

⇒ x² - (α + β)x + αβ.

Put the values in the equation, we get.

⇒ x² - (-3/2)x + (-1) = 0.

⇒ x² + 3x/2 - 1 = 0.

⇒ 2x² + 3x - 2 = 0.

   

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