Question

22. If a and B are zeroes of the polynomial 2y? - 4y + 3, then the value of a?B + aß? is: (2​

Answer 1

Answer:

Given -

α and β are zeroes of polynomial p(y) = 2y² + 7y + 5

To Find -

Value of α + β + αβ

Method 1 :-

→ 2y² + 7y + 5

→ 2y² + 2y + 5y + 5

→ 2y(y + 1) + 5(y + 1)

→ (2y + 5)(y + 1)

Zeroes are -

→ 2y + 5 = 0 and y + 1 = 0

→ y = -5/2 and y = -1

Then,

The value of α + β + αβ is

→ -5/2 + (-1) + (-5/2) × (-1)

→ -5/2 - 1 + 5/2

→ -5 - 2 + 5/2

→ -2/2

→ -1

Method 2 :-

As we know that :-

α + β = -b/a

→ α + β = -(7)/2

→ α + β = -7/2

And

αβ = c/a

→ αβ = 5/2

Then,

The value of α + β + αβ is

→ -7/2 + 5/2

→ -7 + 5/2

→ -2/2

→ -1

Hence,

The value of α + β + αβ is -1

Step-by-step explanation: