Question

obtain all other zeroes of 3x⁴+6x³-2x²-10x-5,if two of its zeros are √5/3 and -5/3.
this question is in the 10class. please solve the problem give me a photo​

Answer 1

Given :

• The given Polynomial is 3x⁴ + 6x³ - 2x² - 10x - 5, and it's given that two of it's zeroes are $\sqrt{ \frac{5}{3} }$ and $- \sqrt{ \frac{5}{3} }$

To Find :

• All the other zeroes.

We are given with two zeroes already, by Multiplying them we get,

${x}^{2} - \frac{5}{3} = {3x}^{2} - 5$

Let us divide 3x² - 5 with the given Polynomial.

Have a look at the attachment!

Now solving the Quotient that we got,

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

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

$x(x + 1) + 1(x + 1) = 0$

${(x + 1)}^{2} = 0$

$\boxed{\sf{x = 1 \: \: and \: \: x = 1}}$

Now, all the zeroes of the Polynomial 3x⁴ + 6x³ - 2x² - 10x - 5 are 1, 1, $\sqrt{ \frac{5}{3} }$ and $- \sqrt{ \frac{5}{3} }$