Question

)A quadratic polynomial, whose zeroes are -4 and -5, is *​

Answer 1

EXPLANATION.

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.

                                                                                                                       

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.

Answer 2

x² + 9x + 20

Step-by-step explanation:

QUESTION :-

A quadratic polynomial, whose zeroes are - 4 and - 5, is

_______________________

SOLUTION :-

Let the two zeroes as

α = -4 & β = -5

So,

Sum of zeroes (S) = α + β

=> -4 + (-5)

=> - 4 - 5

=> - 9

=> S = - 9

Product of zeroes (P) = αβ

=> (-4)(-5)

=> 20

=> P = 20

________________________

Now,

To find the quadratic polynomial, we use formula -

x² - (S)x + P

=> x² - (-9)x + 20

=> x² + 9x + 20

So,

The quadratic polynomial is x² + 9x + 20.

_________________________

hope it helps.

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