Which one of the following is the quadratic equation whose roots are reciprocal to the roots of the quadratic equation $2 x^{2} - 3 x - 4 = 0$

3 x^{2} - 2 x - 4 = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

3 x^{2} - 4 x - 2 = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $4 x^{2} + 3 x - 2 = 0$
Given the quadratic equation $2 x^{2} - 3 x - 4 = 0$ .......(1).
Now the quadratic equation whose roots are reciprocal of the roots of the equation (1) will be obtained by replacing $x$ by $\frac{1}{x}$ in (1).

Then the equation will be,

$\frac{2}{x^{2}} - \frac{3}{x} - 4 = 0$

or, $4 x^{2} + 3 x - 2 = 0$ .

Suggest Corrections

Similar questions

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

{4 x}^{2} - 12 x + 9 = 0

4 \sqrt{{3 x}^{2}} + 5 x - 2 \sqrt{3} = 0

3 x^{2} + 7 x + 2 = 0

{(x + 3)}^{2} + 4 x + 7 = 0

2 x^{2} - 8 x + 34 = 0

x^{2} + 2 \sqrt{3 x} - 1 = 0

- 2 x^{2} + 3 x - 4 = 0

2 x^{2} - 3 x + 5 = 0

3 x^{2} - 4 \sqrt{3} x + 4 = 0

2 x^{2} - 6 x + 3 = 0

Join BYJU'S Learning Program