math
posted by Sara .
A polynomial function function is defined by the equation p(x)=3x3+ax2+bx+7, where a, bE/. If p(2)=5 and p(1)=14 then the value of a+b is...

math 
Reiny
From p(2)=5 and p(1)=14
we have two points (2,5) and (1,14)
so,
3(8) + a(4) 2b + 7 = 5
4a  2b = 22 > 2a  b = 11
3(1) + a(1) + b(1) + 7 = 14 > a + b = 4
adding:
3a = 15
a = 5, then b = 1
a+b = 51 = 4
Respond to this Question
Similar Questions

calculus
A cubic polynomial function f is defined by f(x)= 4x^3+ab^2+bx+k where a, b, k, are constants. The function f has a local minimum at x=2 A. Fine the vales of a and b B. If you integrate f(x) dx =32 from o to 1, what is the value of … 
Calculus
A cubic polynomial function f is defined by f(x) = 4x^3 + ax^2 + bx + k? 
Calculus
A cubic polynomial function f is defined by f(x) = 4x^3 + ax^2 + bx + k? 
Calculus
Find the quadratic polynomial g(x)=ax2+bx+c which best fits the function f(x)=7x at x=0, in the sense that g(0)=f(0), and g'(0)=f'(0), and g''(0)=f''(0). 
Clueless in calculus
The function f is defined by f(x)= (25x^2)^(1/2) for 5 less than or = x less than or = 5 A) find f'(x) B) write an equation for the tangent to the graph of f at x=3 C) let g be the function defined by g(x)= (f(x) for 5<or=x<or=3)and … 
Calc
The function f is defined by f(x)= (25x^2)^(1/2) for 5 less than or = x less than or = 5 A) find f'(x) B) write an equation for the tangent to the graph of f at x=3 C) let g be the function defined by g(x)= (f(x) for 5<or=x<or=3)and … 
maths
When the function f(x) is equal to 2xn + ax2  6 is divided by (x1), the reminder is 7 and when divided by (x+3), the reminder is 129. Calculate the value of "a" and "n" and hence write the polynomial function completely. 
Math
0.08x^3 + 0.6x+2.8 absolutevalue function Rational function Another polynomial function Quadratic function 
Math
A quadratic function is defined by f(x)=3.7x^2+6.8x+4.2. A linear function is defined by g(x)=0.5x+k. Determine the value of k so that the line intersects the parabola at exactly one point. Write your answer to the nearest hundredth 
Math
A function f is defined by the equation f(x)=4x−8. Suppose that the state variables T and Q are related by this function according to the mapping f:Q↦T. Suppose that T=3. Use the equation of the function to find the value …