If - - are the roots of 2 x 2-3 x -1-0- then the equation whose roots are 1- 1- isA- 2 x2-x-1-0B- x2-3 x-2-0C- x 2-3 x -2-0D- 2 x2-x-1-0

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Relation between Roots and Coefficients for Quadratic

If α, β are t...

Question

If $α, β$ are the roots of $2 x^{2} + 3 x + 1 = 0$ , then the equation whose roots are $\frac{1}{α}, \frac{1}{β}$ is

x^{2} + 3 x + 2 = 0

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x^{2} - 3 x + 2 = 0

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2 x^{2} + x + 1 = 0

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2 x^{2} - x + 1 = 0

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Solution

The correct option is A $x^{2} + 3 x + 2 = 0$
$f (x) = 2 x^{2} + 3 x + 1 = 0 has roots α, β$
The equation whose roots are $\frac{1}{α}, \frac{1}{β}$ is,
$f (\frac{1}{x}) = 0$
$\Rightarrow \frac{2}{x^{2}} + \frac{3}{x} + 1 = 0 \Rightarrow 2 + 3 x + x^{2} = 0 \Rightarrow x^{2} + 3 x + 2 = 0$

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If α,β are the roots of 2x2+3x+1=0, then the equation whose roots are 1α,1β is

The correct option is A x2+3x+2=0f(x)=2x2+3x+1=0 has roots α,β The equation whose roots are 1α,1β is, f(1x)=0 ⇒2x2+3x+1=0⇒2+3x+x2=0⇒x2+3x+2=0

If $α, β$ are the roots of $2 x^{2} + 3 x + 1 = 0$ , then the equation whose roots are $\frac{1}{α}, \frac{1}{β}$ is

The correct option is A $x^{2} + 3 x + 2 = 0$
$f (x) = 2 x^{2} + 3 x + 1 = 0 has roots α, β$
The equation whose roots are $\frac{1}{α}, \frac{1}{β}$ is,
$f (\frac{1}{x}) = 0$
$\Rightarrow \frac{2}{x^{2}} + \frac{3}{x} + 1 = 0 \Rightarrow 2 + 3 x + x^{2} = 0 \Rightarrow x^{2} + 3 x + 2 = 0$