Question

If alpha and beta are zeros of polynomial x square - 6 X + a find a if beta is equal to minus 2

Answer 1

Answer:

8

Given:

α and β are zeroes of x² + 6x + a

β = -2

To find:

value of a

Step-by-step explanation:

As, β is root of x² + 6x + a it must satisfy the equation.

and β = -2

    so,

    ⇒ (-2)² + 6(-2) + a = 0

    ⇒ 4 - 12 + a = 0

    ⇒ -8 + a = 0

     ⇒ a = 8

Hence, a = 8

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Answer 2

The value of a is -16.

Step-by-step explanation:

Given:

Polynomial $x^{2} -6x+a$.

$\alpha \ and \ \beta$ are zeros of polynomial.

$\beta =-2$

To Find:

The value of a.

Solution:

As given, polynomial $x^{2} -6x+a$.

Polynomial equation $x^{2} -6x+a$ and   are zeros or roots  of polynomial.

$Sum \ of \ roots = -\frac{Coffiecient of \ x}{Coffiecient of \ x^{2} }$

$\alpha +\beta =-\frac{(-6)}{1} =6$  ----------- equation no.01.

As given,$\beta =-2$.

Putting the value of $\beta$ in equation no.01.

$\alpha +(-2) = =6\\\alpha -2=6\\\alpha =8$

The roots of equation $\alpha =8\ and\ \beta =-2$.

$Product \ of \ roots = \frac{Coffiecient of \ constant}{Coffiecient of \ x^{2} }$

$\alpha \times\beta = \frac{a}{1} }$

$8\times(-2)=a$

$a=-16$

Thus,the value of a is -16.

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