Question

questions -

1. if one zero of the polynomial 2x^2 - 5x - (2k + 1) is twice the other, then find both the zeroes and the value of k.

2. solve for x and y :
(a + 2b)x + (2a - b)y = 2
(a - 2b)x + (2a + b)y = 3

3. Find 'a' and 'b'for which this equation have infinite solutions.
(a + b)x - 2by = 5a + 2b + 1
3x - y = 14

4. A boat goes 20 km upstream and 44km downstream in 10 hr. In 13hr, it can go 40 km upstream and 55km downstream . determine the spped of stream and that of boat in still water.
No need to send solution of last, just tell whether the answers are one of the 2 and 8, but please tell the method, and how to tackle some similar questions like the last one.


Please give the answers step by step and not for only points.

Answer 1

ans of 1 to 3 attached. may ask any clarification. what is required for qno. 4

Answer 2

1st and 2nd


3rd solution
(a+b)x -2by=5a+2b+1
3x-y = 14
solution ...........
for infinitelymany solutions
a1/a2=b1/b2=c1/c2
here a1 = a+b
a2= 3
b1=-2b
b2= -1
c1= 5a+2b+1
c2=14
By putting the values
we get , a+b/3=2b =(5a+2b+1) /14
1st take a+b/3= 5a +2b+1/14
on sloving further we get
a=-3+8b
putting a in a+b/3=2b
we get b =1
now putting b in
a= -3+8b
we get a= 5
therefore a=5 and b =1