Question

mere pyare friends plz jldi se yh question solve KR do✌️✌️​

Answer 1

p(x) = 3x⁴ + 6x³ - 2x² - 10x - 5

g(x) = Product of zeroes

$</p><p>\rightarrow \quad \left( x + \sqrt{\frac{5}{3}} \right) \left( x - \sqrt{\frac{5}{3}} \right) \\ \\ \rightarrow \quad x^{2} \cancel{- \sqrt{\frac{5}{3}}x} \cancel{+ \sqrt{\frac{5}{3}}} - \left( \sqrt{\frac{5}{3}} \right)^{2} </p><p></p><p>\\ \\ </p><p></p><p>\rightarrow \quad x^{2} - \frac{5}{3} \qquad \mathtt{ Multiply \: by \: 3 } \\ \\</p><p></p><p>\rightarrow \quad 3x^{2} - 5 </p><p></p><p>$

So,

➜ g(x) = 3x² - 5

g(x) is a factor of p(x) since g(x) is the product of its zeroes, So it will divide complete leaving a quadratic polynomial as quotient and 0 as remainder.

So, On dividing p(x) by g(x) we get quotient as f(x)

Refer to the attachment for division step.

After dividing p(x) by g(x) we get f(x) as x² + 2x + 1

f(x) = x² + 2x + 1

➜ x² + x + x + 1

➜ x(x + 1 ) + 1(x + 1)

➜ (x + 1)(x + 1)

Therefore, Its other two zeroes are -1 and -1

Hence All the zeroes of this polynomial p(x) is -1 , -1 , $\sqrt{\frac{5}{3}} \: , \: - \sqrt{\frac{5}{3}}$