If a and b are the zeroes of the quadratic polynomial 2x²-5x+7. Find the polynomial whose zeroes are 2a +3b and 3a +2b
Answers
Answer: x2-25/2x+41
Step-by-step explanation: 2x2-5x+7
= a + b = 5/2 &
= a*b = 7/2
the sum of the zeroes:
a + b = (2a + 3b) + (3a + 2b)
= 5(a + b)
= 5×5/2
= 25/2
the product of the zeroes:
a*b = (2a +3b) (3a + 2b)
= 6a2 + 6b2 + 13ab
= 6a2 +6b2 +12ab+ab
= 6(a2 +b2+2ab) +ab
= 6(a + b)2 + ab
=6(5/2)2 + 7/2
= 75/2 + 7/2
= 41
hence , the required polynomial g(x) is given by
g (x) = k(x2-sx+p)
k(x2-25/2x+41)
where k is any non zero real number
hope it will clear your doubt