Question

find a quadratic polynomial the sum and product of whose zeroes are1/4 and -1/8 respectively

Answer 1

Answer:

8x^2-2x-1

Step-by-step explanation:

Let the zeroes be m and n respectively and the polynomial be ax^2+bx+c

We know that m+n=(-b/a)

and (m)(n)=c/a

ATQ,

m+n=1/4

=> -b/a=1/4

=> -b/a=2/8

So we can take b as -2 and a as 8

and,

(m)(n)=(-1/8)

=> c/a=(-1/8)

So we can take c as -1 and a as 8. Since the value of a comes the same in both cases, we know that it is correct and so are the values of b and c.

∴ The polynomial is ax^2+bx+c, where a=8, b=(-2) and c=(-1)

∴ The polynomial is 8x^2-2x-1