Question

find the quadratic polynomial whose sum is 9 product is -12​

Answer 1

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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Answer 2

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.