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 [tex]3x^2-12x-11[/tex], writing the equation in the form [tex]3(x+a)^2+b[/tex] using the completing the square method.
[tex]3x^2-12x-11=0\\x^2-\frac{12}{3}x-\frac{11}{3} =0\\x^2-4x-\frac{11}{3} =0\\(x^2-4x+4)-4-\frac{11}{3}=0\\(x-2)^2-\frac{23}{3} =0\\3(x-2)^2-23=0[/tex]
Compare the result with [tex]3(x+a)^2+b[/tex];
a = -2
b = -23
Hence the value of a and b from the expression are -2 and -23 respectively.
b) Given the quadratic equation [tex]3x^2-12x-11=0[/tex] using the general formula to factorize the equation;
[tex]x=\frac{-b\pm \sqrt{b^2-4ac} }{2a} \\x=\frac{-(-12)\pm \sqrt{(-12)^2-4(3)(-11)} }{2(3)} \\x=\frac{12\pm \sqrt{144+132} }{6} \\x=\frac{12\pm\sqrt{276} }{6} \\x=2\pm\sqrt{\frac{276}{36} }\\x=2\pm\sqrt{\frac{23}{3} } }[/tex]
Compared with c ± √d, the value of c and d are 2 and 23/3 respectively.
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