Find the polynomial whose zeroes are and 4
Asked by admin @ in Math viewed by 274 People
)A quadratic polynomial, whose zeroes are -4 and -5, is *
Asked by admin @ in Math viewed by 274 People
)A quadratic polynomial, whose zeroes are -4 and -5, is *
Answered by admin @
Quadratic polynomial.
Whose zeroes are = - 4 and - 5.
As we know that,
Let one zeroes be = - 4 = α.
Other zeroes be = - 5 = β.
Sum of the zeroes of the quadratic polynomial.
⇒ α + β = - b/a.
⇒ - 4 + (-5) = - 9.
⇒ α + β = - 9. - - - - - (1).
Products of the zeroes of the quadratic polynomial.
⇒ αβ = c/a.
⇒ (-4) x (-5) = 20.
⇒ αβ = 20. - - - - - (2).
As we know that,
Formula of quadratic polynomial.
⇒ x² - (α + β)x + αβ.
Put the values in the equation, we get.
⇒ x² - (-9)x + (20).
⇒ x² + 9x + 20.
(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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