Question

pleaseeeeeeeee answer it quickly it's urgent .
Find a quadratic polynomial divisible by (2x - 1) and (x + 3) and which leaves remainder 12
on division by (x - 1).
​

Answer 1

1) It must be a(2x-1)(x+3) for some number a

a(2x-1)(x+3) = a(2x²+5x-3)

If x = 1 rem = a(2 + 5 - 3) = 4a (= 12) so a = 3

So its a(2x-1)(x+3) = 3(2x²+5x-3) = 6x²+15x-9

2)You can do the donkey work for this one, but

a + b = - q/p

ab = r/p

You need the sum of the roots in terms of p, q and r:

a + 1/b + b + 1/a = (a + b) + 1/b + 1/a

= (a + b) + (a+b)/ab = -q/p + (-q/p)/(r/p)

and the product

(a + 1/b )(b + 1/a)

3) Call it ax²+bx + c

When you sub in 1 for x you get 1 so

a+b+c = 1.....(1)

When you sub in 2 for x you get 2 so

4a+2b+c = 2.....(2)

When you sub in 3 for x you get 4 so

9a+3b+c = 4.....(3)

(2)-(1)

3a+b=1

(3)-(2)

5a+b=2

Answer 2

Answer:

here is your answer..........