1.

the sum and products of the zeroes of a quadratic polynomial are -1/2 and-3 respectively.what is the quadratic polynomial

Answer»

\huge\underline\mathbb{\red S\pink{O}\purple{L} \blue{UT} \orange{I}\green{ON :}}

GIVEN that,

  • Sum of the zeroes : α + ß = -1/2
  • Product of the zeroes : αß= - 3

We KNOW that, the FORM of quadratic polynomial is

☯ x² - (α + ß)X + αß = 0

  • Substitute the zeroes.

⟹ {x}^{2}  - ( -  \frac{1}{2} ) + ( - 3) = 0

⟹ {x}^{2}  +  \frac{1}{2}  - 3 = 0

⟹ \frac{2 {x}^{2} + 1 - 6 }{2}  = 0

⟹2 {x}^{2}  + 1 - 6 = 0 \times 2

⟹ {2x}^{2}  + 1 - 6 = 0

\underline{\boxed{\bf{\orange{∴ The\;quadratic\;polynomial\;is\;“ \: 2x² + 1 - 6 = 0  \: ”.}}}}\:\red{\bigstar}

Step-by-step explanation:

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