Question

Find the quadratic polynomials, the sum and product of whose zeros are -3 and 2
respectively​

Answer 1

x^2+x-6

Step-by-step explanation:

S = -3

P= 2

p(x) = x^2-Sx+p

x^2+3x+2

Brainliest plsAnswer:

Answer 2

$\large{\underline{\bf{\pink{Answer:-}}}}$

✰ the required polynomial

⠀⠀⠀⠀⠀⠀ f(x) = x² + 3x + 2

$\large{\underline{\bf{\blue{Explanation:-}}}}$

✰✰ If α and β are the zeroes of

p(x) = ax² + bx + c , a ≠ 0 then

➩⠀(α + β) = - b/a

➩⠀αβ = c/a

⠀

✰✰ A quadratic polynomial whose zeroes are α and β is given by

➩⠀p(x) = [x² - (α + β)x + αβ]

$\large{\underline{\bf{\green{Given:-}}}}$

✰ Sum of zeroes = -3

✰ product of zeroes = 2

$\large{\underline{\bf{\green{To\:Find:-}}}}$

✰. we need to find the quadratic polynomial.

$\huge{\underline{\bf{\red{Solution:-}}}}$

➜ Let α and β are zeroes of required polynomial f(x).

Then,

➜ (α + β) = -3

➜ (αβ) = 2

So,

➩⠀⠀⠀⠀⠀ f(x) = x² - (α + β)x + αβ

➩⠀⠀⠀⠀⠀⠀⠀= x² - (-3)x + 2

➩⠀⠀⠀⠀⠀⠀⠀= x² + 3x + 2 ⠀⠀⠀

So , the required polynomial

⠀⠀⠀⠀⠀⠀f(x) = x² + 3x + 2

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