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