Question

find the value of the polynomial at the indicated value of variable p(x)=3x^2-4x-root 11 at x=2

Answer 1

x^2+bx+12=0
a, coefficient of x^2=1
b, coefficient of x=b
c, constant in the quadratic polynomial=12

Let α,βα,β be the two factors of the equation.

(1) x-3 is a factor of x^2+bx+12.

α=3α=3
αβ=ca=121αβ=ca=121
β=123=4β=123=4

α+β=−ba=−b1α+β=−ba=−b1
b=−7b=−7
Sufficient.

(2) 4 is a factor of x^2+bx+12=0
Same as statement 1.

β=4β=4
αβ=ca=121αβ=ca=121
α=124=3α=124=3

α+β=−ba=−b1α+β=−ba=−b1
b=−7b=−7
Sufficient.

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