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If one root of the equation 2x2 ax 6=0 is 2 the a=?
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If one root of the equation 2x2 ax 6=0 is 2 the a=?
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Let's begin by understanding the quadratic equation and its roots. A quadratic equation is a polynomial equation of the second degree. It can be written in the standard form as:


ax2 + bx + c = 0


where a, b, and c are constants and x is the variable. The roots of a quadratic equation are the values of x that satisfy the equation, i.e., they make the equation true. There are two roots of a quadratic equation, which can be real or complex.


Given Equation


Now, let's consider the given equation:


2x2 - ax + 6 = 0


We are told that one of the roots of this equation is 2. Let's use this information to find the value of a.


Finding the Second Root


Since the equation has two roots, we can use the following formula to find the second root:


x = (-b ± √(b2 - 4ac)) / 2a


Here, b = -a, a = 2, and c = 6 (from the given equation).


Substituting these values in the formula, we get:


2 = (-(-a) ± √((-a)2 - 4(2)(6))) / 2(2)


Simplifying this expression, we get:


2 = (a ± √(a2 - 48)) / 4


Multiplying both sides by 4, we get:


8 = a ± √(a2 - 48)


Finding the Value of a


Now, we have two equations based on the two possible values of the second root:


8 = a + √(a2 - 48)

8 = a - √(a2 - 48)


Squaring both sides of each equation, we get:


64 = a2 - 48 + 2a√(a2 - 48)

64 = a2 - 48 - 2a√(a2 - 48)


Adding 48 to both sides of each equation, we get:


112 = a2 + 2a√(a2 - 48)

112
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If one root of the equation 2x2 ax 6=0 is 2 the a=?
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If one root of the equation 2x2 ax 6=0 is 2 the a=?
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