Question

mx²-2x+p=0 have equal roots find the value of m
and p

Answer 1

Answer:

The value of m = 1/p

The value of p = 1/m

Step-by-step explanation:

f(x) = mx² - 2x + p = 0 has equal roots.

Then the discriminant b² - 4ac = 0

Therefore b²- 4ac = (-2)² - 4mp = 0

=> 4 - 4mp = 0

or 4mp = 4

=> mp = 1

Which implies that, 'm' is the reciprocal of p

or m = 1/p

Roots of the equation = (-b + or - √b² - 4ac) ÷ 2a

= (-(-2) + or - 0) ÷ 2m

= 2/2m => 1/m

Roots of the equation are [1/m , 1/m] or [p, p]

Therefore, the value of m = 1/p

& the value of p = 1/m

The equation can have any values, but, value of p must be the reciprocal of m and vice versa.