Question

Find the zeroes of the following quadratic polynomials and verify the relation ship between the zeroes and the co efficient 2 root 2 x2-9x+5root 2

Answer 1

STEP BY STEP SOLUTION......

FOR ZEROES LET THE POLYNOMIAL p(x)= 0...

$2 \sqrt{2} x {}^{2} - 9x + 5 \sqrt{2} = 0 \\ 2 \sqrt{2} x {}^{2} - (5 + 4) x + 5 \sqrt{2} = 0 \\ 2 \sqrt{2} x {}^{2} - 5x - 4x + 5 \sqrt{2} = 0 \\ x(2 \sqrt{2}x - 5) - \sqrt{2} (2 \sqrt{2} x - 5) = 0 \\( 2 \sqrt{2}x - 5)(x - \sqrt{2} ) = 0 \\ now \\ 2 \sqrt{2} x - 5 = 0 \: and \: x - \sqrt{2} = 0 \\ x = 5 \div 2 \sqrt{2} \: and \: x = \sqrt{2}$

VERIFICATION

now we have two zeroes x = 5/2root and x = root 2

$1)sum \: of \: zeroes \\ - b \div a = (5 \div 2 \sqrt{2} ) + \sqrt{2}(take \: lcm) \\ - ( - 9) \div 2 \sqrt{2} =( 5 + 4) \div 2 \sqrt{2} \\ 9 \div 2 \sqrt{2} = 9 \div 2 \sqrt{2} \\ lhs = rhs \\ \\ now \\ 2)product \: of \: zeroes \\ c \div a = (5 \div 2 \sqrt{2}) \times \sqrt{2} \\ 5 \sqrt{2} \div 2 \sqrt{2} = 5 \div 2 \\ 5 \div 2 = 5 \div 2 \\ lhs \: = rhs$

HENCE PROVED....

I HOPE THIS WILL HELP U ....