find the quadratic polynomial whose sum is 9 product is -12
Answers
Step-by-step explanation:
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Given : Sum of the zeroes of polynomial 9
and,
the product of zeroes of polynomial is 1/9
Therefore,
➡ The required quadratic polynomial is
==> x² - (sum of the zeroes)x + (product of zeroes)
==> x² - (9)x + (1/9)
==> x² - 9x + 1/9
==> 9x² - 81x + 1 ....[ by multiplying whole equation by 9]
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EXPLANATION.
Sum of the zeroes = 9.
Products of the zeroes = - 12.
As we know that,
Sum of the zeroes of the quadratic polynomial.
⇒ α + β = - b/a.
⇒ α + β = 9. - - - - - (1).
Products of the zeroes of the quadratic polynomial.
⇒ αβ = c/a.
⇒ αβ = - 12. - - - - - (2).
As we know that,
Formula of the quadratic polynomial.
⇒ x² - (α + β)x + αβ.
Put the values in the equation, we get.
⇒ x² - (9)x + (-12).
⇒ x² - 9x - 12.
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.