Suppose the roots of the equation 2x^2−5x−6=0 are α and β.find the quadratic equation with roots 1/α and 1/β.

A quadratic equation is represented as: .

The required quadratic equation is:

The equation is given as:

Divide through by 2

So, we have:

--- (1)

And:

--- (2)

Divide (1) by (2)

Split

Take inverse of

So, the equation with roots 1/α and 1/β is:

This gives

Hence, the quadratic equation is:

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6x² + 5x - 2 = 0

Step-by-step explanation:

Given

2x² - 5x - 6 = 0 ← in standard form

with a = 2, b = - 5, c = - 6, then

sum of roots α + β = - =

product of roots = = - 3, then

sum of new roots = +

=

= = -

product of new roots = ×

= = -

Hence the required equation is

x² + x - = 0 or

6x² + 5x - 2 = 0 ( multiplying through by 6 )

answer is b

step-by-step explanation:

answer: sorry i dont really know but can we talk all my friends r gone and im bored

step-by-step explanation: