Question

verify that 1, 2, 3/2 are the zeros of the cubic polynomial p(x)=2x^3-9x^2+13x-6. then verify the relationship between the zeros and the coefficients of the polynomial. ​

Answer 1

The relationship between the zeros and the coefficients of the polynomial is - (-9/2)  = - (coefficient of x^2 / coefficient of x^3)  and - (-6/2) = - (constant term / coefficient of x^3)

• Given,
• p(x)=2x^3-9x^2+13x-6
• =(2x-3)(x^2-3x+2)
• =(2x-3)(x-1)(x-2)
• when
• p(x)=0
• ⇒(2x-3)(x-1)(x-2) = 0
• ⇒x=1,2,3/2
• now,
• sum of roots,
• =1+2+3/2
• =9/2
• =- (-9/2)
• = - (coefficient of x^2 / coefficient of x^3)
• now,
• product of roots,
• =1*2*3/2
• =6/2
• =-(-6/2)
• = - (constant term / coefficient of x^3)

Answer 2

Step-by-step explanation:

you can find the explanation in the above picture