Question

if x=-2 is the root of the equation √2(x+p)=0 and is also the zero of the polynomial px​

Answer 1

$\huge{\star{\underline{\underline{\blue{SOLUTION}}}}}$

Substituting x= -2 in √2(x + p) = 0 , we get

√2(-2 + p) = 0

-2√2 + √2p = 0

√2p = -2√2

p = -2

Substituting p = -2 and x = -2 in

px²+kx+2√2 we get

-2(-2)² + k(-2) +2√2 = 0

-8 - 2k + 2√2 = 0

-2k = - 2√2 + 8

2k = 2√2 - 8

2k = 2(√2 - 4)

$k = \frac{2( \sqrt{2 } - 4)}{2}$

=> k = (√2 - 4)