Question

If the roots of the equation hxsquare + 21x + 10=0, where h is not equal to zero,are in the ratio 2:5,find the possible values of h

Answer 1

Answer:

h=9

Step-by-step explanation:

p(x)=hx²+21x+10

a=h,b=21,c=10

D=b²-4ac

D=(21)²-(4×h×10)

D=441-40h         --------------{eq 1}

now,

α= (-b+√D)/2a    ,   β=(-b-√D)/2a

since it is given that α/β=2/5

therefore, 5α=2β

5[(-b+√D)/2a]=2[(-b-√D)/2a]

-5b+ 5√D = -2b-2√D

7√D=3b            

49D²=9b²

D²=9/49b²

441-40h=9/49×441                       {substituting eq 1 and b=21}

441-40h=81

441-83=40h

360=h×40

h=9

i really hope this is right.sorry for typing