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

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Updated on: September 25th, 2023

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 in x is a second-degree polynomial, or one of the following forms: ax2 + bx + c = 0, where a, b, and c are real values. Before attempting to solve polynomial equations, candidates should write them in standard form. Once the factors have all been calculated and reached zero, set each variable factor to zero. The answers to the derived equations are the solutions to the original equations.

## x2 − 6x + a. Find the Value of ‘a’ if 3α + 2β = 20.

The question states If α and β are zeroes of the quadratic polynomial x2 − 6x + a; find the value of ‘a’ if 3α + 2β = 20. When a variable term in the polynomial expression has the highest power of 2, the polynomial is said to be quadratic. Only the variable’s exponent is considered 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. The steps to solve the given quadratic polynomial are as follows:

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.

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.

Summary:

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

The value of ‘a’ if 3α + 2β = 20 is -16. If α and β are zeroes of the quadratic polynomial x2 − 6x + a. A quadratic equation or function is created when a quadratic polynomial equals 0. Any polynomial can be easily solved using fundamental algebraic ideas and factorization techniques. The first step in solving the polynomial equation is to set the value of the right-hand side to zero.

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