Question

find the quadratic equation whose roots are are reciprocals of the roots of the equation 3x²-20x+17=0

Answer 1

First of all,we will find the roots of the given equation.
 3x²-20x+17=0
⇒3x²-3x-17x+17=0
⇒3x(x-1)-17(x-1)=0
⇒(3x-17)(x-1)=0
⇒x=17/3 or x=1.

Now,roots of the unknown quadratic equation will be 3/17 and 1.
As we all know that quadratic equation p(x)=x²-Sx+P = 0.
    {where S is the sum of the roots and P is the product of roots}

∴ S= 3/17 + 1
∴ S= 20/7

And P= 3/17 × 1
 ∴ P= 3/17

⇒Equation will be :
                              x² - 20/17x + 3/17 = 0
On multiplying the whole equation by 17,we get the required equation;
                            17x² - 20x + 3 = 0
{If we do not multiply the equation by 17 on both sides,then also answer will be correct.}