Find all the zeros of the polynomial 2x⁴ + 7x - 19x² - 14x + 30, if

1.	Find all the zeros of the polynomial 2x⁴ + 7x - 19x² - 14x + 30, if two of its zeroes are √2 and -√2can anyone plss explain in notebook??
Answer» $\huge\purple{\boxed{\underline{ANSWER}}}$ GIVEN THAT:- $➪$ polynomial = 2x⁴ + 7x3 - 19x² - 14x + 30 = $➪$ two of its zeroes are √2 and -√2 EXPLANATION:- Given that √2 and -√2 are two zeros of this polynomial so, $➪$ . (X - √2) and ( x + √2) will be TOW factor of this polynomial as well as $➪$ (x-√2)( x+√2) = ( x² - 2 ) will be also the factor of Given polynomial . Now dividing the polynomial with ( x² - 2 ) $⟶ \: \: \frac{2 {x}^{4} + 7 {x}^{3} - 19 {x}^{2} - 14x + 30 }{ {x}^{2} - 2 } \\ \\ ⟶ \: \: 2 {x}^{2} + 7x - 15 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$ Now we get a quadratic equation so $⟶ \: \: 2 {x}^{2} + 7x - 15 \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ ⟶ \: \: 2 {x}^{2} + 10x - 3x - 15 \\ \\ ⟶ \: \: 2x(x + <klux>5</klux>) - 3(x + 5) \\ \\ ⟶ \: \: (x + 5)(2x - 3) \: \: \: \: \: \: \: \: \: \: \\ \\ ⟶ \: \: x = - 5 \: and \: \frac{3}{2 } \: \: \: \: \: \: \: \: \: \: \: \: \:$ Now the all zeros of Given polynomial √2 , - √2 , -5 and 3/2 . Thanks

Find all the zeros of the polynomial 2x⁴ + 7x - 19x² - 14x + 30, if two of its zeroes are √2 and -√2can anyone plss explain in notebook??

Answer»

$\huge\purple{\boxed{\underline{ANSWER}}}$

GIVEN THAT:-

$➪$ polynomial = 2x⁴ + 7x3 - 19x² - 14x + 30 =

$➪$ two of its zeroes are √2 and -√2

EXPLANATION:-

Given that √2 and -√2 are two zeros of this polynomial so,

$➪$ . (X - √2) and ( x + √2) will be TOW factor of this polynomial

as well as

$➪$ (x-√2)( x+√2) = ( x² - 2 ) will be also the factor of Given polynomial .

Now dividing the polynomial with ( x² - 2 )

$⟶ \: \: \frac{2 {x}^{4} + 7 {x}^{3} - 19 {x}^{2} - 14x + 30 }{ {x}^{2} - 2 } \\ \\ ⟶ \: \: 2 {x}^{2} + 7x - 15 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Now we get a quadratic equation

$⟶ \: \: 2 {x}^{2} + 7x - 15 \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ ⟶ \: \: 2 {x}^{2} + 10x - 3x - 15 \\ \\ ⟶ \: \: 2x(x + <klux>5</klux>) - 3(x + 5) \\ \\ ⟶ \: \: (x + 5)(2x - 3) \: \: \: \: \: \: \: \: \: \: \\ \\ ⟶ \: \: x = - 5 \: and \: \frac{3}{2 } \: \: \: \: \: \: \: \: \: \: \: \: \:$