Question

The difference of roots is 9 and sum of their square is 13,find the quadratic equation

Answer 1

Answer:

plzzz give me brainliest ans and plzzzz follow me

Answer 2

Given :

Difference of roots = 9

Sum of their squares = 13

To find : the quadratic equation =?

Solution:

Let the roots be $a$ and $b$

Difference of roots :

$a-b=9$-----(1)

Sum of their squares :

$a^2+b^2=13$  -----------(2)

Using Eq(1) and eq(2) :

Squaring the equation (1) we get :

$(a-b)^2=9^2\\\\a^2+b^2-2ab=81\\\\13-2ab=81\\\\-2ab=81-13\\\\-2ab=68\\\\ab=\dfrac{-68}{2}=-34$

Now, using Eq(2) we get :

$a^2+b^2+2ab=13+2ab\\\\(a+b)^2=13-68\\\\(a+b)^2=-55\\\\a+b=\sqrt{55}i$

So, the quadratic equation becomes:

$x^2-\sqrt{55}ix-34$