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

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

Answer 2

Answer:

Given:

a , ß 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 roots = -b/a

$\longrightarrow$a + ß = -(-8)/1

$\longrightarrow$ a + ß = -- equation (1)

product of roots = c/a

$\longrightarrow$aß = a/1

$\longrightarrow$ aß = a -- equation (2)

it is also gien that,

$\longrightarrow$a² + ß² = 40

using a²+b²=(a+b)²-2ab in LHS we get,

$\longrightarrow$(a+ß)²- 2aß=40

substituting the respective value from equation (1) , (2) we get,

$\longrightarrow$8² - 2a =40

$\longrightarrow$64 - 40=2a

$\longrightarrow$24/2 = a

$\longrightarrow$a=12

therefore ,

the value of a is 12.