Question

if a beta are the two zeros of the polynomial f y is equal y square-8y+a and a square+beta squar is equal to 40 find the value of a​

Answer 1

Answer:-

Given:-

α , β are the roots of p(y) = y² - 8y + a.

On comparing the given polynomial with the standard form of a quadratic equation i.e., ax² + bx + c = 0 ;

Let,

• a = 1
• b = - 8
• c = a.

We know that,

Sum of the roots = - b/a

⟹ α + β = - ( - 8)/1

⟹ α + β = 8 -- equation (1).

Product of the roots = c/a

⟹ αβ = a/1

⟹ αβ = a -- equation (2)

It is also given that,

⟹ α² + β² = 40

using a² + b² = (a + b)² - 2ab in LHS we get,

⟹ (α + β)² - 2αβ = 40

Substituting the respective values from equations (1) & (2) we get,

⟹ 8² - 2a = 40

⟹ 64 - 40 = 2a

⟹ 24/2 = a

⟹ a = 12

∴ The value of a is 12.

Answer 2

Given :-

α and β are zeroes of f(y) = y² - 8y + a

To Find :-

Value of a

Solution :-

We know that

Sum of zeroes = -b/a

By putting value

α + β = -(-8)/1

α + β = 8/1

α + β = 8

Now

αβ = c/a

αβ = a/1

αβ = a

Now

(α + β) = 40

α² + β² + 2αβ = 40

Taking 2 as common

(α + β)² + 2αβ = 40

(8)² + 2(a) = 40

(64) + 2a = 40

2a = 64 - 40

2a = 24

a = 24/2

a = 12