## if X and B are the zeros of the qaudratic polynomial f(x)=x2-3x+2,then find x2+b2​

Question

if X and B are the zeros of the qaudratic polynomial f(x)=x2-3x+2,then find x2+b2​

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1 month 2021-08-19T08:25:23+00:00 1 Answer 0 views 0

If m and n are the zeroes of

To find :

zeroes are 1/(2m+n) and 1/(2n+m) .

Explanation:

Compare f(x)= x²-3x-2 with

ax²+bx+c, we get

a = 1 , b = -3 , c = -2

i) m+n = -b/a = -(-3)/1 = 3–(1)

ii) mn = c/a = -2/1 = -2–(2)

iii) m²+n² = (m+n)²-2mn

= 3² – 2×(-2)

= 9 + 4

= 13 —-(3)

Now ,

1/(2m+n) , 1/(2n+m) are zeroes

of a polynomial.

1) Sum of the zeroes

= 1/(2m+n) + 1/(2n+m)

= [2n+m+2m+n]/[(2m+n)(2n+m)]

= [3m+3n]/[4mn+2m²+2n²+mn]

= [3(m+n)]/[2(m²+n²)+5mn]

= [3×3]/[2×13 + 5(-2)]

= 9/(26-10)

= 9/16 —-(4)

2) Product of the zeroes

= [1/(2m+n) × 1/(2n+m)]

= 1/( 4mn+2m²+2n²+mn)

= 1/[2(m²+n²) + 5mn ]

= 1/[ 2×13 + 5(-2)]

= 1/(26-10)

= 1/16 —(5)

______________________

is

k[x²-(sum of the zeroes)x+product of the zeroes]

______________________

Here ,

Required polynomial is

k[ x²-(9/16)x+1/16]

For all real values of k it is true.

let k = 16,

16[x²-(9/16)x+1/16]

= 16x²-9x+1

Therefore,

Polynomial whose zeroes are

1/(2m+n) and 1/(2n+m) is

16x²-9x+1

hope it helps u