Question

This is the question

Answer 1

p(x) = 4x² + 5√2x - 3

Comparing with the standard form of quadratic polynomial (i.e., ax² + bx + c , we get:

a = 4, b = 5√2 , c = -3

We know,

$\qquad \sf \boxed{ \sf x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} }$

So,

$\sf \rightarrow \quad x = \dfrac{ - 5 \sqrt{2} \pm \sqrt{ {(5 \sqrt{2} )}^{2} - 4 \cdot - 3 \cdot 4 } }{2 \times 4} \\ \\ \sf \rightarrow \quad x = \frac{ - 5 \sqrt{2} \pm \sqrt{50 - 48} }{8} \\ \\ \sf \rightarrow \quad x_{1} = \frac{ - \cancel{4} \sqrt{2} }{ \cancel{8}_{2} } \quad \: : \quad x_{2} = \frac{ - \cancel{ 6}^{3} \sqrt{2} }{ \cancel{8}_{4}} \\ \\ \sf \rightarrow \quad x = \frac{- \sqrt{2} }{2} \: \: , \: \: \frac{ - 3 \sqrt{2} }{4}$