Question

if alpha and beta are the roots of x^2+7x+11=0 then the equation of the roots (alpha + beta)^2 and (alpha - beta)^2 is?​

Answer 1

Answer:

1)49

2)5

Step-by-step explanation:

Hope you understand!

Answer 2

Answer:

The quadratic equation with the given roots is $x^{2}-54x+245=0$

Step-by-step explanation:

Given that,

α and β are the roots of the equation $x^{2}+7x+11=0$ and we are required to find the equation with the roots $(\alpha +\beta )^{2}\:$ and $(\alpha -\beta )^{2}\:$.

We know that for any quadratic equation $ax^{2}+bx+c=0$ the sum of its roots is $-\frac{b}{a}$ and the product of its roots is $\frac{c}{a}$.

Hence for the equation $x^{2}+7x+11=0$,

$\alpha +\beta =\frac{-7}{1} =-7= > (\alpha +\beta )^{2}=49\\\alpha \beta =\frac{11}{1} =11$

Now the difference of the roots is found as follows

$(\alpha -\beta )^{2}=(\alpha +\beta )^{2}-4\alpha \beta \\=(-7)^{2}-4(11)=49-44=5$

Therefore

$(\alpha +\beta )^{2}=49\\(\alpha -\beta )^{2}=5$

Now the quadratic equation with above roots is

$(x-(\alpha +\beta )^{2})(x-(\alpha -\beta )^{2})\\= > (x-49)(x-5)=0\\= > x^{2}-54x+245=0$

Therefore,

The quadratic equation with the given roots is $x^{2}-54x+245=0$

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