Which of the following statements are true about the equation below?x^2-6x+2=0( 1 ) The graph of the quadratic equation has a minimum value.( 2 ) The extreme value is at the point (3,-7).( 3 ) The extreme value is at the point (7,-3).( 4 ) The solutions are x = -3 + or - the square root of 7 .( 5 ) The solutions arex = 3 + or - the square root of 7.( 6 ) The graph of the quadratic equation has a maximum value.
Accepted Solution
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Answer: Option 1, 2, 5 are the correct answer.Explanation: We have the quadratic equation, [tex]x^2-6x+2=0[/tex] First derivative of the equation is given by 2x - 6 = 0 So x = 3 At x = 3 the value of quadratic equation is extreme, corresponding y is given by [tex]3^2-6*3+2=11-18=-7[/tex], So extreme value is at (3,-7) Second derivative of the quadratic equation is given by 2 ( positive value) Second derivative is positive so graph of equation has a minimum value. Now root of the equation [tex]x^2-6x+2=0[/tex] is given by [tex]\frac{6+\sqrt{(-6)^2-4*1*2}} {2} =3+\sqrt{7}[/tex] or [tex]\frac{6-\sqrt{(-6)^2-4*1*2}} {2} =3-\sqrt{7}[/tex]Option 1, 2, 5 are the correct answer.