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

Answer:

The value of a is -16.

Step-by-step explanation:

Given :

• α and β are zeroes of the quadratic polynomial x² - 6x + a

• 3α + 2β = 20

To find :

the value of a

Solution :

From the relation between zeroes and coefficients of quadratic polynomial,

Sum of zeroes = -(x coefficient)/x² coefficient

 Product of zeroes = constant/x² coefficient

For the given quadratic polynomial,

• x² coefficient = 1

• x coefficient = -6
• constant = a

Sum of zeroes = -(-6)/1

α + β = 6 ➟ [1]

Also given,

3α + 2β = 20

α + 2α + 2β = 20

α + 2(α + β) = 20

α + 2(6) = 20

α + 12 = 20

α = 20 - 12

α = 8

Substituting α = 8 in equation 1,

α + β = 6

8 + β = 6

β = 6 - 8

β = -2

Now, product of zeroes = a/1

  αβ = a

8 × (-2) = a

 a = -16

Therefore, the value of a is -16