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

By Ritesh|Updated : November 9th, 2022

The value of 'a' if 3α + 2β = 20 is -16. Steps to solve the given quadratic polynomial:

Given that: α and β are the zeroes of the quadratic polynomial x2 − 6x + a and 3α + 2β = 20, then we must determine a's value.

The process is as follows.

α + β = - (-6)/1

In simplification we get the:

α + β = 6 ….. (1)

αβ = a/1

The above equation can be written as:

αβ = a….. (2)

3α + 2β = 20

Taking common

2(α + β) + α = 20

Substituting the values from equation 1 we get:

2 x 6 + α = 20

α = 8

Now, we are putting the value α in equation (1), and we get:

8 + β = 6

β = -2

From equation (2), we have:

a = 8 x (-2)

a = -16

Hence the value of a is −16.

Quadratic Polynomial

  • When a variable term in the polynomial expression has the highest power of 2, the polynomial is said to be quadratic.
  • Only the exponent of the variable is taken into account when determining a polynomial's degree.
  • It is not taken into account how strong a coefficient or constant term is.
  • The roots or zeros of the quadratic equation are the names given to the solutions of such an equation.

Summary:

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

If α and β are zeroes of the quadratic polynomial x2 − 6x + a; the value of 'a' if 3α + 2β = 20 is -16. A quadratic equation or quadratic function is created when a quadratic polynomial is equal to 0.

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