Question

Find the roots of root2 x square + 7x +5 root2=0​

Answer 1

$x = - \sqrt{2} \\ x = - \frac{5 \sqrt{2} }{2}$

Step-by-step explanation:

$p(x) = \sqrt{2} {x}^{2} + 7x + 5 \sqrt{2} = 0 \\ factors \: of \: 5 \sqrt{2} \: are \: ±1 \: ± \sqrt{2} \: ±5 \\ p( - \sqrt{2} ) = \sqrt{2} {( - \sqrt{2}) }^{2} + 7( - \sqrt{2} ) + 5 \sqrt{2} \\ = 2 \sqrt{2} - 7 \sqrt{2} + 5 \sqrt{2} \\ = 0 \\ x = 0 \\ p(x) \div (x + \sqrt{2} ) = \sqrt{2} x + 5 \\ \sqrt{2} x + 5 = 0 \\ \sqrt{2} x = - 5 \\ x = - \frac{5}{ \sqrt{2} } = - \frac{5 \sqrt{2} }{2}$