Question

Find the equation whose roots are larger by 2 than the roots of the equation x2 - 4x + 3 = 0.....( plzz tell me..)​

Answer 1

Answer:

The given equation is:

x^2 - 4x + 3 = 0

Let's find the roots of the given equation by factorisation meathod.

Thus , we have;

=> x^2 - 4x + 3 = 0

=> x^2 - 3x - x + 3 = 0

=> x(x - 3) - (x - 3) = 0

=> (x - 3)(x - 1) = 0

=> x = 1 , 3

It is given that, the roots of the required equation are larger by 2 than the roots of the given equation.

Thus , the roots of the required equation are: x = (1+2) , (3+2)

ie, x = 3 , 5.

Also,

Note that ,a quadratic equation is given as:

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

Here,

For the required quadratic equation:

sum of roots = 3+5 = 8

product of roots = 3•5 = 15

Thus,

The required quadratic equation is:

x^2 - 8x + 15 = 0