Question

Find the quadratic equation with integral coefficients whose roots are thrice the roots of the quadratic equation x²-8x+1=0

Answer 1

Answer:

The required equation is

x² - 24x + 9 = 0

Solution:

The given equation is

x² - 8x + 1 = 0

If p and q be the roots of the given equation, then

p + q = - ( - 8)/1 = 8

pq = 1/1 = 1

Then 3 (p + q) = 24

or, 3p + 3q = 24 ..... (1)

and 9pq = 9

or, (3p) (3q) = 9 ..... (2)

ATQ, 3p and 3q are the roots of the required equation, then the required equation be

x² - (3p + 3q) x + (3p) (3q) = 0

or, x² - 24x + 9 = 0