Question

If alpha and beta are the zeroes of the polynomial p(x)=x²-6x+a.Find the value of ‘a’.If 3alpha + 2beta =20.​

Answer 1

Given, α and β are zeroes of the quadratic polynomial 2 − 6 +

Now, α + β = 6 ......1

Given, 3 + 2 = 20 ........2

Multiply by 3 in equation 1, we get

3α + 3β = 18 ......3

Subtract equation 2 and 3, we get

(3α + 2β) - (3α + 3β) = 20 - 18

=> 3α + 2β - 3α - 3β = 2

=> -β = 2

=> β = -2

From equation 1, we get

α + (-2) = 6

=> α - 2 = 6

=> α = 6 + 2

=> α = 8

Now, product of the zeroes = a/1

=> 8 * (-2) = a

=> a = -16

So, the value of a is -16

Answer 2

Given, α and β are zeroes of the quadratic polynomial 2 − 6 +

Now, α + β = 6 ......1

Given, 3 + 2 = 20 ........2

Multiply by 3 in equation 1, we get

3α + 3β = 18 ......3

Subtract equation 2 and 3, we get

(3α + 2β) - (3α + 3β) = 20 - 18

=> 3α + 2β - 3α - 3β = 2

=> -β = 2

=> β = -2

From equation 1, we get

α + (-2) = 6

=> α - 2 = 6

=> α = 6 + 2

=> α = 8

Now, product of the zeroes = a/1

=> 8 * (-2) = a

=> a = -16

So, the value of a is -16