Question

37. Find a quadratic polynomial of the given numbers are the sum and product of its zeroes respectively. -1/4,-1​

Answer 1

Step-by-step explanation:

P(x) = x² + 2x + 1

Let P(x) = 0

Substituting this value

0 = x² + 2x + 1

By splitting the middle term

0 = x² + (1 +1) x + 1

0 = x² + x + x +1

0 = x (x+1) + 1(x +1)

0 = (x+1) (x+1)

\therefore∴ x + 1 = 0

x = -1

Hence , the zeroes are as :

\alpha = -1α=−1

and \beta = -1β=−1

Relations between zeroes and coefficient of polymers in a quadratic equation ax² + bx + c

Here a = 1 , b = 2 and c =1

Sum of zeroes = -b/a

- 1 + (-1) = - 2/1

-2 = -2

Product of zeroes = c/a

-1 × (-1) = 1/1

1 = 1