1.

The sum and product of the zeroes of a quadratic polynomial are 3 and -10 respectively the quadratic polynomial is

Answer»

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

  • ✦ sum of zeroes = 3
  • ✦ product of zeroes = -10

\large{\underline{\bf{\red{To\:Find:-}}}}

\huge{\underline{\bf{\green{Solution:-}}}}

LET α and β be the zeroes of the REQUIRED polynomial p(x).

Then

  • (α + β) = 3
  • αβ = -10

So,

p(x) = x² -(α + β)x + αβ

➝ p(x) = x² - 3x -10

So, the required polynomial is x² - 3x -10.

Verification:-

Sum of zeroes:-

(α + β) = - b/a

➝ 3 = -(-3)/1

➝ 3 = 3

Product of zeroes:-

αβ = c/a

➝ -10 = -10/1

➝ -10 = -10

LHS = RHS

hence, verified

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