Question

if the roots of 9x^2+3mx+4=0are equal the find the value of m​

Answer 1

Answer:

roots of 9x^2+3mx+4=0 are equal

ax^2+bx+c=0 in this equation,

if the roots are equal then

b^2-4ac=0

similarly,

in above equation b=3m, a=9.c=4

so,

(3m)^2-4.9.4=0

=> 9m^2=144

=> m^2=144/9

=> m^2=16

=> m=√16

=> m=+4, -4

Answer 2

Step-by-step explanation:

given a = b

then p(x) = x² - x (a + b) + ab

given p(x) = 9x² + 3mx + 4 = 0

dividing throughout by 9 to make coefficient of x² as 1, we get

x² + 3mx/9 + 4/9 = 0

x² + m/3 x + 4/9 = 0

on comparing both, we get

m/3 = a + b________1

4/9 = ab___________2

as a = b, from equation 2, a² = 4/9 => a = ± 2/3 and b = ± 2/3

substituting in equation 1,

m/3 = 2/3 + 2/3 [ a and b positive ]

m = 3*4/3

m = 4

also m/3 = - 2/3 - 2/3 [ and and b are negative ]

m = 3* (-4/3)

m = - 4