Question

Find the polynomiai if zeroes are -3/2 and 2/3​

Answer 1

Answer:

6x² + 5x - 6

Step-by-step explanation:

Quadratic Polynomial = x² - (α + β)x + αβ

where:

• (α + β) is the sum of zeroes
• αβ is the product of zeroes.

First, let's find Sum of zeroes:

$\sf{Sum \: of \: zeroes = \dfrac{-3}{2}+\dfrac{2}{3}}$

$\implies \sf{Sum \: of \: zeroes=\dfrac{2}{3}-\dfrac{3}{2}}$

$\implies \sf{Sum \: of \: zeroes = \dfrac{4-9}{6}}$

$\implies \boxed{\sf{Sum \: of \: zeroes = \dfrac{-5}{6}}}$

Now let's find the Product of Zeroes.

$\sf{Product \: of \: zeroes=\dfrac{-3}{2}\times \dfrac{2}{3}}$

$\implies \boxed{\sf{Product \: of \: zeroes=-1}}$

Now put the values of Sum of zeroes and product of zeroes in the above equation of Quadratic Polynomial.

$\sf{Quadratic \: Polynomial = x^{2}-\bigg(\dfrac{-5x}{6}\bigg)+(-1)}$

$\dashrightarrow \: \: \sf{Quadratic \: Polynomial = x^{2}+\dfrac{5x}{6}-1}$

Multiplying by 6 throughout,

$\boxed{\boldsymbol{Quadratic \: polynomial \to 6x^{2}+5x-6}}$