Question

Write a quadriatic polynomial Sum of whose Zeroes is 2 and product is -8​

Answer 1

$\sf{Sum \: \: of \: \: the \: \: zeroes = 2 }\\ \sf{Product \: \: of \: \: the \: \: zeroes = (-8)}$

$\sf{Formula \: \: for \: \: quadratic \: \: Polynomial = } \\ \boxed{ \sf{x²-(sum \: \: of \: \: the \: \: zeroes ) \: x + (product \: \: of \: \: the \: \: zeroes )}}$

$\tt{x²-(2)x + (-8) }\\ \\ \boxed{ \tt{x²-2x-8}}$

$\color{purple}{ \bf{Hope \: \: this \: \: helps \: \: you \: !}}$

Answer 2

Answer:

⇒ Given zeros are α=2 and β=−6.

⇒ Sum of zeros =α+β=2+(−6)=−4

⇒ Product of zeros =α×β=2×(−6)=−12

⇒ Quadratic polynomial =x

2

−(α+β)x+(α×β)

⇒ Quadratic polynomial =x

2

−(−4)x+(−12)

∴ Quadratic polynomial =x

2

+4x−12