Question

If alpha and bita are zeros of x2+6x+5 find polynomial whase zeros are 1by alpha and 1 by bita

Answer 1

Answer:-

Alpha is taken as "p" and beta is taken as "q".

Given Polynomial => x² + 6x + 5 = 0.

Let , a = 1 , b = 6 , c = 5.

We know that,

Sum of the roots = - b/a

→ p + q = - (6)/1

→ p + q = - 6 -- equation (1).

Product of the roots = c/a

→ pq = 5/1

→ pq = 5 -- equation (2).

We know that,

General form of a quadratic equation is x² - (sum of zeroes)x + (product of zeroes) = 0

The zeroes of new quadratic polynomial are 1/p , 1/q. So,

→ x² - (1/p + 1/q)x +(1/p)(1/q) = 0

→ x² - [(p + q)/pq]x + (1/pq) = 0

Putting the values from equation (1),

→ x² - ( - 6/5)x + 1/5 = 0

→ x² + 6x/5 + 1/5 = 0

Taking LCM,

→ (5x² + 6x + 1)/5 = 0

→ 5x² + 6x + 1 = 0.

Hence, the new quadratic equation formed will be 5x² + 6x + 1 = 0.