Find the equation whose roots are less by3,than those 3x^2-7x+6=0
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Given :-
equation is f(x) = x3 + 3x2 – 7x + 6 = 0
Required equation :-
is f(√x) = 0
⇒ x√x + 3x – 7√x + 6 = 0
⇒ √x(x – 7) = – (3x + 6)
Squaring on both sides,
⇒ x(x – 7)2 = (3x + 6)2
⇒ x(x2 – 14x + 49) = 9x2 + 36 +36x
⇒ x3 – 14x2 + 49x – 9x2 – 36x – 36 = 0
i.e. x3 – 23x2 + 13x – 36 = 0
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