what is the sum and product of a quadratic polynomial whose zeroes are 2 and -10 respectively?
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EXPLANATION.
Zeroes of the quadratic polynomial = 2 and - 10.
As we know that,
Let one zeroes be = α = 2.
Other zeroes be = β = - 10.
Sum of the zeroes of the quadratic polynomial.
⇒ α + β = - b/a.
⇒ 2 + (-10).
⇒ 2 - 10 = - 8.
⇒ α + β = - 8.
Products of the zeroes of the quadratic polynomial.
⇒ αβ = c/a.
⇒ (2)(-10) = - 20.
⇒ αβ = - 20.
As we know that,
Formula of the quadratic polynomial.
⇒ x² - (α + β)x + αβ.
Put the values in the equation, we get.
⇒ x² - (-8)x + (-20).
⇒ x² + 8x - 20.
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.
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