Question

if a and b are the zeroes of the polynomial 2y2+7y+5 then find the value of alpha+ beta +alpha beta​

Answer 1

Answer:

sum of zeroes = alpha + beta = -b/a = -7/2

product of zeroes = alpha*beta = c/a = 5/2

alpha+beta+alpha*beta = (-7/2) + (5/2) =(5-7)/2 = -2/2= -1

Hope this helps you...

Answer 2

Given:-

→ Polynomial : 2y² + 7y + 5

To find:-

→ Value of (α + β) + αβ

Solution 1 :-

First we will find zeros of polynomial by middle term spitting

→ 2y² + 7y + 5 = 0

→ 2y² + 2y + 5y + 5 = 0

→ 2y(y + 1) + 5(y + 1) = 0

→ (y + 1)(2y + 5) = 0

→ y = -1 or 2y = -5

→ y = -1 & y = -5/2

Therefore,

Zeros of polynomial are : -1 & (-5/2)

Here,

• α = -1
• β = -5/2

Now we have to find value of (α + β) + αβ

Putting all values:-

→ (-1 + -5/2) + {-1 × (-5/2)}

→ (-1 - 5/2) + (5/2)

→ (-2 - 5)/2 + (5/2)

→ (-7/2) + (5/2)

→ (-7 + 5)/2

→ -2/2

→ -1

So, required value = -1

$\rule{200}{1}$

Solution 2:-

We can easily find value (α + β) + αβ by using the given polynomial itself.

Polynomial : 2y² + 7y + 5

As we know,

Sum of zeros = α + β = -(coefficient of x)/(coefficient of x²) = -b/a

→ α + β = -7/2

We also know,

Product of zeros = αβ = constant term/coefficient of x² = c/a

→ αβ = 5/2

Therefore,

→ (α + β) + αβ

→ (-7/2) + 5/2

→ (-7 + 5)/2

→ -2/2

→ -1

So, required value : -1 .