Question

Find the quadratic polynomial, the sum of whose zeros is 2 and
their product is -12. Hence, find the zeros of the polynomial.​

Answer 1

Answer:

Here, in this question something is given which we have to write.

Given

ab = -12

a+b=2

Now, firstly we have to write the given things in our solution. Then we should apply p(x) = x² - sum(x) + Product which is correctly equal to = x² - 2x - 12 = 0 which is a type of an quadratic equation by which we have to find the value of x.

So,

The sum of zeroes=2

The product of zeroes=-12

By applying the formula of p(x), we get the correct and accurate value of x.

p(x)=x² - (sum)x + product

=x² - 2x - 12

we will do middle splitting term now.

=> x² - 2x - 12 = 0

=> x² - 4x + 3x - 12 = 0

=> x(x-4)+3(x-4)=0

=> (x-4)(x+3)=0

.°. x=4,-3

Therefore, the two zeroes are (4) and (-3).

Answer 2

Answer:

.Let S and P denotes respectively the sum and product of the zeros of a polynomial are \(2 \sqrt{3}\) and 2. Hence, the quadratic polynomial is \(g(x)=k\left(x^{2}-2 \sqrt{3} x+2\right)\)where k is any non-zero real number.