Question

can you find out a^2+b^2​

Answer 1

${x}^{2} + ax + b$

is divided by x=1 then the remainder is 15

ATQ

${x}^{2} + ax + b \\ {(1)}^{2} + 1 \times a + b = 15 \\ 1 + a + b = 15 \\ a + b = 15 - 1 \\ a + b = 14 \: \: \:(i)$

and

${x}^{2} + bx + a$

is divided by x = -1 then the remainder is -1

ATQ

${x}^{2} +b x + a \\ {( - 1)}^{2} + b \times (- 1) + a = - 1 \\ 1 - b + a = - 1 \\ a - b = - 1 - 1 \\ a - b = - 2 \\ a = b - 2 \: \:( ii)$

putting the value of a in equation ii

$a + b = 14 \\ b - 2 + b = 14 \\ 2b = 14 + 2 \\ 2b = 16 \\ b = 8$

then a

$a = b - 2 \\ a = 8 - 2 \\ a = 6$

${a}^{2} + {b} ^{2} \\ {(6)}^{2} + {(8)}^{2} \\ 36 + 64 \\ 100$