Question

find zeros of following quadratic polynomial and verify the relationship between zero and the coefficient 2 x square - 9 X + 4​

Answer 1

given quadratic polynomial, 2x² - 9x + 4

now, 2x² - 9x + 4 = 0

or, 2x² - 8x - x + 4 = 0

or, 2x(x - 4) - 1(x - 4) = 0

or, (2x - 1)(x - 4) = 0

x = 1/2 , 4

hence, zeros of given polynomial are ; 1/2 and 4 .

verification :

sum of zeros = -coefficient of x/coefficient of x²

LHS = sum of zeros = 1/2 + 4 = 9/2

RHS = -coefficient of x/coefficient of x²

= -(-9)/2 = 9/2

LHS = RHS

hence verified.

again, product of zeros = constant/coefficient of x²

LHS = product of zeros = 1/2 × 4 = 2

RHS = constant/coefficient of x² = 4/2 = 2

LHS = RHS

hence verified.