Find the equation whose roots are reciprocals of the roots of 2 x 2-5 x -4-0-A- 2 x2-4 x-5-0B- 5 x2-4 x-2-0C- 4 x2-5 x-2-0D- 4 x2-2 x-5-0

The correct option is C To get the equation, whose roots are reciprocals, replace x by 1/x. ⇒2 ×1/x^2+5/x+4=0 Multiplying by x^2, ⇒ 2+5x+4x^2 =0 or ...

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Standard XII

Mathematics

Harmonic Progression

Find the equa...

Question

Find the equation whose roots are reciprocals of the roots of $2 x^{2} + 5 x + 4 = 0$ .

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Solution

The correct option is C

To get the equation, whose roots are reciprocals, replace x by $\frac{1}{x}$ .

$\Rightarrow 2 \times \frac{1}{x^{2}} + \frac{5}{x} + 4 = 0$

Multiplying by $x^{2}$ ,

$\Rightarrow 2 + 5 x + 4 x^{2} = 0 o r 4 x^{2} + 5 x + 2 = 0$

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Find the equation whose roots are reciprocals of the roots of 2x2+5x+4=0 .

The correct option is C To get the equation, whose roots are reciprocals, replace x by 1x. ⇒2×1x2+5x+4=0 Multiplying by x2, ⇒2+5x+4x2=0 or4x2+5x+2=0

Find the equation whose roots are reciprocals of the roots of $2 x^{2} + 5 x + 4 = 0$ .

The correct option is C

To get the equation, whose roots are reciprocals, replace x by $\frac{1}{x}$ .

$\Rightarrow 2 \times \frac{1}{x^{2}} + \frac{5}{x} + 4 = 0$

Multiplying by $x^{2}$ ,

$\Rightarrow 2 + 5 x + 4 x^{2} = 0 o r 4 x^{2} + 5 x + 2 = 0$