Question

Find the relationship between zeroes and coefficients of the polynomial x2+8x+15=0

Answer 1

a=1,b=8,c=15

x=(-b+-√(b*b-4ac))/2a

x=(-8+-√64-60)/2

x=(-8+-√4)/2

x=-8+-2/2

x=-8+2/2

x=-6/2

x=-3

or

x=-8-2/2

x=-10/2

x=-5

Answer 2

Polynomial Rules

• a + ß = - Coefficient of x/Coefficient of x²
• aß = Constant Term/Coefficient of x²

______________________________

➵ p(x) = x² + 8x + 15

➵ 0 = x² + 3x + 5x + 15

➵ 0 = x(x + 3) + 5(x + 3)

➵ 0 = (x + 3)(x + 5)

➵ x = - 3 and - 5

______________________________

➵ a + ß = - (+ 8)/1

➵ - 3 + (- 5) = - 8/1

➵ - 8 = - 8

➵ L.H.S = R.H.S

&

➵ aß = 15/1

➵ - 3 × (- 5) = 15

➵ 15 = 15

➵ L.H.S = R.H.S

Hence relation verified