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Maths-

General

Easy

Question

$x squared minus 12 x plus 23 equals 0$
Which of the following is a solution to the given equation?

$- 12 + \sqrt{11}$
$12 + \sqrt{11}$
$- 6 + \sqrt{13}$
$6 + \sqrt{13}$

The correct answer is: $6 plus square root of 13$

HINT : - Find roots using quadratic formula
Explanation:
If the equation $a x squared plus b x plus c equals 0$ is given then roots of the quadratic equation are
$x equals fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction$
Step 1: Here equation is $x squared minus 12 x plus 23 equals 0$ and on comparison with
$a x squared plus b x plus c equals 0$ we get a=1, b=-12 and c=23
Step 2: calculation
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell x equals fraction numerator 12 plus-or-minus square root of left parenthesis negative 12 right parenthesis squared minus 4 left parenthesis 1 right parenthesis left parenthesis 23 right parenthesis end root over denominator 2 left parenthesis 1 right parenthesis end fraction end cell row cell x equals fraction numerator 12 plus-or-minus square root of 144 minus 92 end root over denominator 2 end fraction end cell row cell x equals fraction numerator 12 plus-or-minus square root of 52 over denominator 2 end fraction end cell row cell x equals fraction numerator 12 plus-or-minus 2 square root of 13 over denominator 2 end fraction end cell row cell x equals 6 plus-or-minus square root of 13 end cell end table$
The roots of the equation $x squared minus 12 x plus 23 equals 0 text are end text 6 plus square root of 13 text and end text 6 minus square root of 13$

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