Question

If α and β are the zeroes of the quadratic polynomial p(x) = 2x2 – 5x + 7, find a quadratic polynomial whose zeroes are 2α + 3β and 2β + 3α. It would be appreciated if you would provide an explanation along with the solution!

Answer 1

Answer:

sum of zeroes -b/a=5/2

product of zeroes c/a =7/2

Step-by-step explanation:

sum of zeroes is 25/2

product of zeroes is 76

p(x) = x²-25/2x +76

Answer 2

Step-by-step explanation:

At first take the GIVEN polynomial as p(x) and for this polynomial find the sum and product of the roots and take them as eqn 1 and 2 respectively.

Then find the sum of the GIVEN roots by substituting equation 1 we get 25/2.

Next product of the GIVEN roots by substituting equation 2 we get 41.

finally substitute the sum and product of the GIVEN roots in general polynomial structure and you will get the answer.