Question

If 1/5 and – 2 are respectively product and sum of the zeroes of a quadratic polynomial. Find the polynomial. This is a grade 10 NCERT problem.

Answer 1

GIVEN:

Product of the zeroes = 1/5

Sum of zeroes = -2

TO FIND:

The quadratic polynomial

SOLUTION:

We know that,

The standard form of quadratic polynomial is,

k {x² - (sum of zeroes)x + product of zeroes}

Where, k ≠0

=> k {x² - (-2)x + (1/5)

=> k {x² + 2x + 1/5}

When k = 5

=> 5(x² + 2x + 1/5)

=> 5x² + 10x + 1

Therefore, the required polynomial is 5x² + 10x + 1.

Answer 2

Answer:

x² + 2 x + 1 / 5

Step-by-step explanation:

Given :

Sum of zeroes α + β = - 2

Product of zeroes α β = 1 / 5

We are asked to find quadratic polynomial :

We know :

Required polynomial = x² - ( α + β ) x + α β

Putting values here we get :

Required polynomial = x² - ( - 2 ) x + 1 / 5

= > Required polynomial = x² + 2 x + 1 / 5

Hence we get required answer.