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:

Heya Blinkue!

Explanation:

Alpha and beta are the zeroes of the polynomial of y^2 - 8y + a.

So, alpha + beta = 8

Thus, alpha^2 - 8alpha + a = 0 ------ 1

Beta^2 - 8beta+ a = 0----------2

Adding equation 1 and 2 , we get,

Alpha^ 2 - 8 alpha + a + beta^2 - 8beta + a =

alpha^2 + beta^ 2 - 8( alpha + beta) + 2a = 0

40 - 8(8) + 2a=0

40- 64= -2a

-24=-2a

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.