Question

from a quadratic polynomial whose zeroes are 5 and-5

Answer 1

Hey there!!

Here's your answer..

If α and β are the zeroes of a quadratic equation, the equation can be written as

x² - x (α + β) + αβ = 0

Here, the zeroes are 5 and -5

Let α  = 5 and β = -5

So, α + β = 5 - 5 = 0 and αβ = 5 (-5) = -25

Hence, the quadratic equation is x² - x (0) - 25 = 0

⇒ x² - 25 = 0 is the required equation.


Hope it helps!!

Answer 2

HERE'S YOUR ANSWER
One method has been explained by my friend. I'll do with the second method. _________________________

We know that the general equation of a quadratic equation with roots given can be written as :

(x-a)(x-b) = 0
where 'a' and 'b' are the roots of the given equation.

Therefore, the roots, when put in the generalised equation, give :

[x - (5)].[x - (-5)] = 0

(x-5)(x+5) = 0

Using the identity, we get

x^2 - 25 =0
which is the required equation.
_______________________

HOPE HELPED! !

HAPPY TO HELP :)

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