Question

find a quadric polynomial whose sum and product of zeroes are 0 and √5​

Answer 1

Answer:

x² + √5

Step-by-step explanation:

We must find a Quadratic equation whose Sum = 0 and Product = √5

Let zeroes be a and b

a + b = 0

ab = √5

We know that, such an equation do exist.

and its general formula is

x² - (a + b)x + (ab)

= x² - (0)x + (√5)

= x² + √5

OR

We know that,

Sum of zeroes = -b/a = 0

Product of zeroes = c/a = √5

Now,

Let the Quadratic equation be ax² + bx + c

Let's now divide the whole equation by a, so that the coefficient of x² is 1.

(ax²)/a + (bx)/a + c/a = 0/a

x² + (b/a)x + c/a = 0

We can also write this as,

x² - (-b/a) + (c/a) = 0

Here the -ve's cancel out so it's ok

Now, putting in the values

x² - (0)x + (√5) = 0

x² + √5 = 0

Hence,

x² + √5 is the Quadractic equation whose Sum is 0 and product is √5.

Hope it helped and believing you understood it........All the best