Question

Form the quadratic polynomial p(x) whose sum and product of the zeroes are 3 and 2/5.​

Answer 1

Explanation:

x² - (α + β)x + αβ = 0

α+β= 3 +2/5

`=(3*5)/(1*5)+(2)/(5)=(15)/(5)+(2)/(5)\\\\=(17)/(5)`

αβ=3*2/5 = 6/5

`x^(2)-(17)/(5)x+(6)/(5)=0`

Multiply by 5

`5*x^(2)-5*(17)/(5)x+5*(6)/(5)=0\\\\5x^(2)-17x+6=0`