If a and ß are zeroes of x² - 6x + 6 then the
value of a ² +beta
squre is
Answers
If alpha and beta are the zeroes of the quadratic polynomial x^2-x-6, then how would you find the value of alpha^4+beta^4?
Now, if you know [Math Processing Error] and [Math Processing Error], it is very easy to determine the value of the expression [Math Processing Error]. So, how do you find [Math Processing Error] and [Math Processing Error]? Well, you could try looking for simple factors of the quadratic, or you could use the formula for calculating the roots of a quadratic equation or you could form the square. In this particular case, all three methods are very simple.
However, there is a method that you can use for your calculation that doesn’t involving finding [Math Processing Error] and [Math Processing Error]! In this case, it is the more complex way; however, sometimes, it can be quicker.
The trick is to make use of the fact that for the quadratic [Math Processing Error],
[Math Processing Error]
[Math Processing Error]
[If [Math Processing Error] and [Math Processing Error] are the roots of the quadratic, then [Math Processing Error].
Multiplying this out, we have [Math Processing Error]
Equating the coefficients of this quadratic with the initial quadratic, we have:
[Math Processing Error] Equation 1.
[Math Processing Error] Equation 2.]
In our quadratic, [Math Processing Error], [Math Processing Error] and [Math Processing Error], so we have:
[Math Processing Error]
[Math Processing Error]
Now, how does this help us?
Well, [Math Processing Error]
[Math Processing Error]
[Math Processing Error]
[Math Processing Error]