Math, asked by guddimangla1997, 6 months ago

if alpha and beta zeroes of the following quadratic polynomial x^2-x-6 then find the value of a^4+B^4 ​

Answers

Answered by Amanjeets191
1

Answer:

Step-by-step explanation:

Now, if you know  α  and  β , it is very easy to determine the value of the expression  α4+β4 . So, how do you find  α  and  β ? 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  α  and  β ! 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  ax2+bx+c=0 ,

α+β=−ba  

αβ=ca  

[If  α  and  β  are the roots of the quadratic, then  a(x−α)(x−β)=0 .

Multiplying this out, we have  ax2−a(α+β)x+aαβ=0  

Equating the coefficients of this quadratic with the initial quadratic, we have:

−a(α+β)=b→  Equation 1.

aαβ=c→  Equation 2.]

In our quadratic,  a=1 ,  b=−1  and  c=−6 , so we have:

α+β=−−11=1  

αβ=−61=−6  

Now, how does this help us?

Well,  α4+β4=(α2+β2)2−2α2β2  

=((α+β)2−2αβ)2−2α2β2  

=((1)2−2×−6)2−2×(−6)2  

=(1+12)2−72=132−72=169−72=97

Answered by asingh29519
0

Answer:

کی ہے کی ہے کے سے کے سے کی میں ہے سے کے میں کے کی ۹

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