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Transformation of Roots: Algebraic Transformation

Suppose a2=5a...

Question

Suppose $a^{2} = 5 a - 8$ and $b^{2} = 5 b - 8$ . Then the equation whose roots are $\frac{a}{b}$ and $\frac{b}{a}$ is

8 x^{2} + 9 x + 8 = 0

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6 x^{2} - 5 x + 6 = 0

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8 x^{2} - 9 x + 8 = 0

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9 x^{2} - 8 x + 9 = 0

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Solution

The correct option is C $8 x^{2} - 9 x + 8 = 0$
From given conditions
$a, b$ are the roots of $x^{2} - 5 x + 8 = 0$
$\Rightarrow a + b = 5$ , $a b = 8$
Required equation is $x^{2} - (\frac{a}{b} + \frac{b}{a}) x + (\frac{a}{b} . \frac{b}{a}) = 0 \Rightarrow x^{2} - \frac{(a + b)^{2} - 2 a b}{a b} x + 1 = 0 \Rightarrow 8 x^{2} - 9 x + 8 = 0$

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Transformation of Roots: Algebraic Transformation

Standard XII Mathematics

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Suppose a2=5a−8 and b2=5b−8. Then the equation whose roots are ab and ba is

The correct option is C 8x2−9x+8=0From given conditions a,b are the roots of x2−5x+8=0 ⇒a+b=5, ab=8 Required equation is x2−(ab+ba)x+(ab.ba)=0⇒x2−(a+b)2−2ababx+1=0⇒8x2−9x+8=0

Suppose $a^{2} = 5 a - 8$ and $b^{2} = 5 b - 8$ . Then the equation whose roots are $\frac{a}{b}$ and $\frac{b}{a}$ is