Question

If if a and b are the zeros of the polynomial 2ysquare +7y+5 write the value a+b+ab

Answer 1

Step-by-step explanation:

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

Answer 2

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Given:

• We have been given that a and b are the zeroes of the polynomial 2y^2 + 7y + 5.

To Find:

• We need to find the value of a + b + ab.

Solution:

We have been given a polynomial 2y^2 + 7y + 5.

Here, a = 2, b = 7 and c = 5.

As it is given that a and b are two zeroes,

So, sum of zeroes(a + b)

= -b/a

= -7/2___(1)

Product of zeroes(ab)

= c/a

= 5/2___(2)

Now we need to find the value of a + b + ab,

So we have,

a + b + ab = (a + b) + ab

Substituting the values from equation 1 and 2, we get,

(-7/2) + (5/2)

= (-7 + 5)/2

= -2/2

= -1

Therefore, the value of a + b + ab is -1.