Question

Write the quadratic polynomial whose zeroes are 2,-4

Answer 1

Answer:

Step-by-step explanation:

Given zeroes are 2, -4

We all know that x^2- Sx + p

So, x^2 = 1 , Sx = 2 and P = -4

=> x^2 -2 + (-4)

=> x^2 -2x -4

So , quadratic equation is x^2 -2x-4..

Hope this helps you ☺️☺️☺️...

Answer 2

$\large\bf\underline \blue {To \: \mathscr{f}ind:-}$

• » Quadratic polynomial

$\huge\bf\underline \purple{ \mathcal{S}olution:-}$

$\bf\underline{\red{Given:-}}$

• » Zeroes of Quadratic polynomial is given as 2 and - 4.

${ \blue{ \mathscr{ \underline{Let : - }}}}$

⚘ Let α and β are zeroes of required polynomial

• Let α = 2
• and β = -4

✫Sum of zeroes = α + β

↛ α + β = 2 + (-4)

↛ α + β = 2 - 4

↛ α + β = -2 ⠀⠀...1)

✫ Product of zeroes = αβ

↛ αβ = 2 × (-4)

↛ αβ = -8 ⠀⠀...2)

• Formula for quadratic polynomial
• x² - (α + β)x + αβ

Putting values of α + β and αβ from 1) and 2) in this formula , we get,

↛ x² -(-2)x + (-8)

↛ x² + 2x - 8

Hence,

• The quadratic polynomial is x² + 2x - 8.

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