Question

Show that 1/2 and -3/2 are the zeroes of the polynomial 4x 2 +4x-3 and verify the relationship between zeroes and coefficients of polynomials.​

Answer 1

Answer:

$let \: \alpha \: and \: \beta \: be \: the \: zeroes \: of \: the \: polynomial. \\ 4{x}^{2} + 4x - 3 = 0 \\ 4{x}^{2} + 6x - 2x - 3 = 0 \\ 2x(2x + 3) - (2x + 3) = 0 \\ (2x - 1)(2x + 3) = 0 \\ x = \frac{1}{2} , \frac{ - 3}{2} \\ \alpha = \frac{1}{2} , \beta = \frac{ - 3}{2} \\ \alpha + \beta = \frac{ - b}{a} \\ lhs , \alpha + \beta = \frac{1}{2} + \frac{ - 3}{2} = - 1 \\rhs , \frac{ - b}{a} = \frac{ - 4}{4} = - 1 \\ = > \alpha + \beta = 1$

$and \\ \alpha \beta = \frac{1}{2} \times \frac{ - 3}{2} = \frac{ - 3}{4} \\ \frac{c}{a} = \frac{ - 3}{4} \\ = > \alpha \beta = \frac{c}{a}$ [/tex]