Obtain all zeroes of $2 x^{4} + 7 x^{3} - 19 x^{2} - 14 x + 30$ , if two of its zeroes are $\sqrt{2}$ and $- \sqrt{2}$ .

Open in App

Solution

$p (x) = 2 x^{4} + 7 x^{3} - 19 x^{2} - 14 x + 30$
Two of its zeroes are
$\begin{matrix} \sqrt{2} & - \sqrt{2} s o, g (x) = (x - \sqrt{2}) (x + \sqrt{2}) \Rightarrow x^{2} - 2 d i v i s o r = x^{2} - 2 Q u o t i e n t = 2 x^{2} + 7 x - 15 R e m a i n d e r = 0 q (x) = - 2 x^{2} + 7 x - 15 2 x^{2} + 10 x - 3 x - 15 = 0 2 x (x + 5) - 3 (x + 5) = 0 (2 x - 3) (x + 5) = 0 2 x - 3 = 0 2 x = 3 x = \frac{3}{2} x + 5 = 0 x = - 5 s o, r o o t s o f e q u a t i o n i s \sqrt{2}, - \sqrt{2}, \frac{3}{2} & - 5 \end{matrix}$

Suggest Corrections

Similar questions

2 x^{4} + 7 x^{3} - 19 x^{2} - 14 x + 30,

\sqrt{2}

- \sqrt{2} .

\sqrt{2} and - \sqrt{2}

\sqrt{2}

\sqrt{- 2}

p (x) = 2 x^{4} + 7 x^{3} - 19 x^{2} - 14 x + 30 a r e \sqrt{2} a n d - \sqrt{2},

2 x^{4} + 7 x^{3} - 19 x^{2} - 14 x + 30 are \sqrt{2} and - \sqrt{2},

Join BYJU'S Learning Program