Question

Find a quadratic polynomial, the sum and product of whose zeroes are - 1/5 and 1/5 respectively​

Answer 1

Answer:x^2 + x + 1

Step-by-step explanation:general form is

X^2 - (alpha + beta)x + (alpha×beta)

According to the question

Let alpha be = -1/5 and beta be = 1/5

Therefore according to the formula

X^2 - (-1/5)x + (1/5)

X^2 + 1/5x + 1/5

We get x^2 + x + 1

Answer 2

$\huge{\underline{\underline{\bf{Solution}}}}$

$\rule{200}{2}$

$\tt Given\begin{cases} \sf{Sum \: of \: zeroes = \frac{-1}{5}} \\ \sf{Product \: of \: zeroes = \frac{1}{5}} \end{cases}$

$\rule{200}{2}$

$\Large{\underline{\underline{\bf{To \: Find :}}}}$

We have to find the quadratic polynomial.

$\rule{200}{2}$

$\Large{\underline{\underline{\bf{Explanation :}}}}$

We know the formula to find quadratic polynomial when sum and product of zeroes are given

$\Large{\star{\boxed{\rm{Quadratic \: polynomial = x^2 - (sum)x + Product}}}}$

__________________[Put Values]

$\tt{→Quadratic \: polynomial = x^2 - (\frac{1}{-5})x + (\frac{1}{5})} \\ \\ \tt{→Quadratic\: polynomial = x^2 - (\frac{-1}{5})x + \frac{1}{5}} \\ \\ \tt{→Quadratic \: polynomial = x^2 + \frac{1}{5}x + \frac{1}{5}}$