Question

If α and ß are zeros of x ²-x +4 , then find

i) α+ß

ii) αß

iii) 1/α + 1/ß- αß​

Answer 1

Answer:-

Given:

α and β are the roots of x² - x + 4.

Let a = 1 , b = - 1 , c = 4.

We know that,

Sum of the zeroes = - b/a

→ α + β = - ( - 1) / 1

i) α + β = 1 -- equation (1)

Product of the zeroes = c/a

→ αβ = 4/1

ii) αβ = 4 -- equation (2)

iii) 1/α + 1/β - αβ

Taking LCM we get,

→ [ α + β - (αβ)(αβ) ] / αβ

Putting the values of α + β and αβ from equations (1) & (2) we get,

→ [ 1 - 4 * 4 ] / 4

→ [ 1 - 16 ] / 4

→ - 15/4

Hence,

• α + β = 1

• αβ = 4

• 1/α + 1/β - αβ = - 15/4.