Question

If alpha and beta are zeroes of the polynomial t2 – t – 4, form a quadratic polynomial whose zeroes are 1/alpha and 1/beta .

Answer 1

-4t^2-1*t+1=0

Alpha +beta=-(-1)/1
Alpha *beta=-4/1

Now use (x-1/alpha).(x-1/beta)=0 to get equation

Answer 2

Answer:

The equation is $-4t^{2} -t+5=0$.

Step-by-step explanation:

Quadratic equations are the equations of degree two and is in one variable.

It is of the type $f(x) = ax^{2} + bx + c = 0$

$a,b,c$ belong to real numbers.

$a\neq 0$

$a$ is called the leading coefficient.

The given quadratic equation is $t^{2}-t-4=0$

The roots are $\alpha ,\beta$

The sum is $\alpha +\beta =1$

and product

$\alpha \beta =-4$

We are to determine the equation whose roots are $1/\alpha ,1/\beta$

$(x-1/\alpha )(x-1/\beta )=0$

Solving we get

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

Using values

$-4x^{2} -x+5=0$

As the variable is $t$, the required equation is:

$-4t^{2} -t+5=0$

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