Question

If α and β are zeroes of the quadratic polynomial x2 – 6x + a; find the value of ‘a’ if 3α + 2β = 20.

Answer 1

Hi

Here devil1407

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.

Hope it helps u

Thanx........Bye

Answer 2

Step-by-step explanation:

x² - 6x + a

a = 1    b = -6   c = a

α +β = -b/a = 6

αβ = c/a = a

3α + 2β = 20

3α = 20 - 2β  

α = (20 - 2β) / 3

α + β = 6

(20 - 2β)/3 + β = 6

multiplying by 3 on both sides

20 - 2β + 3β = 18

20 + β = 18

β = 18 - 20  

β = -2

α = (20 -2β)/3

α = (20 - 2 × -2)/3

α = (20 + 4)/3

α = 8

αβ =  a  

8 × -2 = a

a = -16

Hope it helps!!

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