Question

It m and n are the zeroes of
2x²-5x+7 Find the quadratic
polymonials whose zeroes are (2m+3n)
and(3m+2n)​

Answer 1

Correct Question:

If m and n are the zeroes of 2x²-5x-7. Find the quadratic polymonial whose zeroes are (2m+3n) and (3m+2n).

Answer:

k(2x^2-25x+68) ; k≠0

Step-by-step explanation:

Given a quadratic polynomial 2x^2-5x-7.

Also, given that,

m and n are the zeroes of it.

Let's find out the zeroes.

Factorising and solving further we get,

=> 2x^2 -7x + 2x - 7 = 0

=> 2x^2 + 2x - 7x - 7 = 0

Taking out common terms, we will get,

=> 2x(x+1)-7(x+1) = 0

=> (x+1)(2x-7) = 0

Therefore, we will get,

=> x + 1 = 0

=> x = -1

And

=> 2x-7 = 0

=> 2x = 7

=> x = 7/2

Therefore, the values of m = -1 and n = 7/2.

Now, we will get,

(2m+3n) = -2+21/2 = (21-4)/2 = 17/2

(3m+2n) = -3+7 = 4

Therefore, we will get,

=> Sum of roots = 17/2+4 = (17+8)/2 = 25/2

=> Product of roots = 4(17/2) = 2(17) = 34

Therefore, we will get new polynomial as,

= x^2 - (25/2)x + 34

= (2x^2-25x+68)/2

= k(2x^2 - 25x + 68)

Hence, the required polynomial is k(2x^2-25x+68) where, k≠0