Question

l+m,l-m find quadratic equation whose roots are​

Answer 1

GIVEN :

Find quadratic equation whose roots are​ l+m, l-m

TO FIND :

The quadratic equation whose roots are​ l+m, l-m

SOLUTION :

Given that l+m, l-m are the roots.

Let $\alpha=l+m$ and $\beta=l-m$ be the given roots.

The formula for a quadratic equation with given roots is :

$x^2-(sum of the roots)x+(product of the roots)=0$

Now $Sum of the roots=\alpha+\beta$

Sum of the roots=l+m+l-m

⇒ Sum of the roots=2l

Now $Product of the roots=\alpha\times \beta$

$=(l+m)\times (l-m)$

By using the algebraic formula :

$(a-b)(a+b)=a^2-b^2$

⇒ $Product of the roots=l^2-m^2$

Now we have to substituting the values in the formula we get

$x^2-(2l)x+(l^2-m^2)=0$

⇒ $x^2-2lx+l^2-m^2=0$

∴ The quadratic equation for the  given roots l+m, l-m is $x^2-2lx+l^2-m^2=0$