Question

If the product of zeroes of the polynomial
ax ² 6x-6 is 4. Find the Value of a'. Find the
Sum of zeroes of the polynomial​

Answer 1

Answer:

a = -3/2

Step-by-step explanation:

Given a quadratic polynomial such that,

ax^2 + 6x - 6.

Also, given that,

Product of zeroes = 4

To find the value of a.

We know that,

In a quadratic polynomial, Ax^2 +Bx + C

Sum of zereos = -B/A

Product of zereos = C/A

Now, in the given question,

Therefore, we will get,

=> -6/a = 4

=> a = -6/4

=> a = -3/2

Hence, required value of a = -3/2.

Answer 2

$\sf{\underline{Answer\::}}$

Value of a = -3/2 or -1.5

Sum of zeores = -4

$\sf{\underline{Explanation\::}}$

We have been allocated with a quadratic polynomial :

• ax² + 6x - 6

whose product of zeroes is 4.

We actually need to decipher for the value of a and also need to figure out the sum of zeroes of the allocated polynomial.

Compare the allocated quadratic polynomial with the basis form,

• Ax² + Bx + C

We have the following values,

1. A = a
2. B = 6
3. C = -6

We have product of zeores known to us. We can use it's value and find a's value.

It is known that product of zeores of polynomial is the constant term of polynomial over the coefficient of x².

=> $\sf{Product\:of\:zeroes\:=\:\dfrac{C}{A}}$

=> $\sf{4\:=\:\dfrac{-6}{a}}$

=> $\sf{4a = -6}$

=> $\sf{a\:=\dfrac{-6}{4}}$

=> $\sf{a\:=\:\dfrac{-3}{2}}$

It is known that, sum of zeroes of a polynomial is the coefficient of x over coefficient of x².

=> $\sf{Sum\:of\:zeroes\:=\:\dfrac{-B}{A}}$

$\sf{=> Sum\:of\:zeroes\:=\:\dfrac{-6}{1.5}....\big[a=\:\dfrac{-3}{2}\:=\:1.5\big]}$

=> $\sf{Sum\:of\:zeroes\:=-4}$