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

Question

Mathematics

Martha Clay

10 June, 10:06

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

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Answers (1)

Know the Answer?

Maverick Vaughan · Answer 1

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