Question

hx^2+kx-6=0 if x=-2,3/4 find the values of h,k

Answer 1

Answer:

the given equation is:

hx^2+kx-6=0

it is given that , x=-2,3/4 are the roots of the given equation,

thus, at x=-2,3/4 the value if the polynomial would become zero.

now, putting x=-2 in the given equation,

we have:

=> h(-2)^2+k(-2)-6=0

=> 4h-2k-6=0

=> 2h-k-3=0

=> k=2h-3 ------(1)

now , putting x=3/4 in the given equation we have:

=> h(3/4)^2+k(3/4)-6=0

=> 9h/16 + 3k/4 - 6=0

=> 9h+12k-96=0------(2)

from equation-(1) and (2)

we have;

=> 9h+12(2h-3)-96=0

=> 9h+24h-36-96=0

=> 33h-132=0

=> 33h=132

=> h=132/33

=> h=4

now, using eq----(1)

we get:

=> k=2h-3

=> k=2(4)-3

=> k=8-3

=> k=5.

thus, the required value of h=4 and k=5.