Question

Find a quadratic polynomial the sum and product of whose zeroes are √2 and -3/2 respectively.Also find its zero

Answer 1

quadratic polynomial will be

x²-(sum of zeroes)x+product of zeroes=0,

x²-√2x+(-3/2) =0,

2x²-2√2x-3=0,

2x²-(3√2-√2)x-3=0,

2x²-3√2x+√2x-3=0,

√2x(√2x-3)+1(√2x-3)=0,

(√2x-3)(√2x+1)=0,

if
√2x-3=0,

then
x=3/√2,

if √2x+1=0,

then

x=-1/√2