Question

a-' + B-
If a, ß are the roots of x^2 - px +q = 0, then alpha-^3 + beta-^3 / alpha^3 + beta^3
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Answer 1

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Asked on December 27, 2019 by

Amba Rawat

If α, β are roots of the equation x

2

+px+q=0, then the equation whose roots are

α

q

,

β

q

will be

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ANSWER

Given α, β are roots of the equation

x

2

+px+q=0

α+β=−p

and αβ=q

Now, sum of roots =

α

q

+

β

q

=

αβ

q(α+β)

⇒ Sum of roots=−p

Product of roots =

α

q

β

q

=

αβ

q

2

⇒ Product of roots =q

So, the required quadratic equation is

x

2

−(−p)x+q=0

x

2

+px+q=0.

Step-by-step explanation:

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