Question

The quadratic polynomial p(x) with -81 and 3 as product and one of the zeroes respectively is: *

1 point

x^2 + 24x - 81

x^2 - 24x - 81

x^2 + 24x + 81

x^2 - 24x + 81

Choose the option.​

Answer 1

Gɪᴠᴇɴ :-

• Product of Roots = (-81)
• One zeroes = 3.

Tᴏ Fɪɴᴅ :-

• The quadratic polynomial ?

ᴄᴏɴᴄᴇᴘᴛ ᴜsᴇᴅ :-

The Quadratic Equation with sum of Roots & Product of roots is given by :-

x² - (sum of Roots)x + Product of Roots = 0

Sᴏʟᴜᴛɪᴏɴ :-

→ Product of Roots = (-81)

→ One zeroes = 3.

→ Other zeroes = (-81/3) = (-27) .

So,

→ sum of Both Zeroes = (-27) + 3 = (-24).

→ Product of Roots = (-81)

Therefore ,

→ The quadratic polynomial = x² - (sum of Roots)x + Product of Roots = 0

→ The quadratic polynomial = x² - (-24)x + (-81) = 0

→ The quadratic polynomial = x² + 24x - 81 = 0 (Ans.)

Hence, The given quadratic polynomial is x² + 24x - 81 = 0.

Answer 2

Step-by-step explanation

$\bf \huge \: \: Given \: \:$

• The quadratic polynomial p(x)
• with -81 and 3 as product
• One of the zeroes respectively is 1 point

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$\bf \huge \: \: To \: Find\:$

• the zeroes respectively is: *
• 1 point
• x^2 + 24x - 81
• x^2 - 24x - 81
• x^2 + 24x + 81
• x^2 - 24x + 81
• Choose the option.

____________________________

Let

Sum of zeroes = (a+b) = -81

Product of zeroes = (a×b) = 3

Other zeros = (-81/3)= -27

then All of zeros= 3+(-27)= -24

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Accourding to the Quadratic Equation:-

$\bf \:X^2 - (a+b)X + (a×b) =0 \:$

Then Putting the value:-

$\bf \: X^2 - (-24).X + (-27×3) = 0 \:$

On multiplying:-

$\bf \red{X^2+24x-81 =0 }\:$

$\bf \red{X^2+24x-81 =0} \:$ Is the required Quadratic equation.

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