a) The quadratic 3x^2-12x-11 can be written in the form 3(x+a)^2+b. Find the values of a and b. b) Given that the solutions of the equation 3x^2-12x-11=0 can be written as c ± √d, where c and d are rational numbers. Find the values of c and d answer for d as a fraction in it's simplest form

a) The value of a and b from the expression are -2 and -23 respectively.

b) The value of c and d are 2 and 23/3 respectively'

a) Given the quadratic function , writing the equation in the form using the completing the square method.

Compare the result with ;

a = -2

b = -23

Hence the value of a and b from the expression are -2 and -23 respectively.

b) Given the quadratic equation using the general formula to factorize the equation;

Compared with c ± √d, the value of c and d are 2 and 23/3 respectively.

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Step-by-step explanation:

a) 3x^2-12x-11=3*x^2-3*2*2*x+3*4-23=3*(x^2-2*2x+2^2)-23=3*(x-2)^2-23

so  a= -2 ,b= -23

b) x1=[12+V(12^2-4*3* -11)]/6=12/6+V(144+132)/6=2+2/6V69=2+1/3V69=

2+V69/9=2+V23/3

c=2, d= 23/3