find a quadratic polynomial the sum and product of whose zeroes are 3 and 2 respectively
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EXPLANATION.
Quadratic equation.
Sum of the zeroes = 3.
Products of zeroes = 2.
As we know that,
Sum of the zeroes of the quadratic equation.
⇒ α + β = -b/a.
⇒ α + β = 3.
Products of the zeroes of the quadratic equation.
⇒ αβ = c/a.
⇒ αβ = 2.
As we know that,
Formula of quadratic polynomial.
⇒ x² - (α + β)x + αβ.
Put the values in the equation, we get.
⇒ x² - (3)x + 2 = 0.
⇒ x² - 3x + 2 = 0.
MORE INFORMATION.
(1) = Real and unequal, if b² - 4ac > 0.
(2) = Rational and different, 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.
Answered by
1
Given,
Sum of zeroes= -3
Product of zeroes= 2
x²+(sum of zeroes)x+(product of zeroes)
=x²+(-3)x+(2)
=x²-3x+2,
Is the required equation
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