Find all the zeros of the polynomial $f (x) = 2 x^{4} - 3 x^{3} - 3 x^{2} + 6 x - 2$ , if two of its zeros are $\sqrt{2}$ and $- \sqrt{2}$ .

\frac{1}{2}, 1

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

\frac{1}{2}, - 1

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

\frac{- 1}{2}, 1

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

\frac{- 1}{2}, - 1

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

Open in App

Solution

The correct option is D $\frac{1}{2}, 1$
$T w o z e r o s a r e \sqrt{2} a n d - \sqrt{2} s o (x - \sqrt{2}) a n d (x + \sqrt{2}) a r e f a c t o r s o r w e c a n s a y (x^{2} - 2) i s a f a c t o r h e n c e t h e o t h e r f a c t o r i s (2 x^{2} - 3 x + 1) n o w t o f i n d r e s t o f z e r o 2 x^{2} - 3 x + 1 = 0 2 x^{2} - 2 x - x + 1 = 0 2 x (x - 1) - 1 (x - 1) = 0 (x - 1) (2 x - 1) = 0 ∴ x = 1 o r x = (\frac{1}{2})$

Suggest Corrections

Similar questions

\frac{1}{2}

2 x^{4} - 3 x^{3} - 3 x^{2} + 6 x - 2

\sqrt{2}

- \sqrt{2}

2 + \sqrt{3} and 2 - \sqrt{3}

p (x) = 2 x^{4} - 3 x^{3} - 3 x^{2} + 6 x - 2

\sqrt{- 2}

\sqrt{2}

\sqrt{2}

- \sqrt{2}

Join BYJU'S Learning Program