Question

Find the serwes of the polynomial
f (x) = 4√3 x² + 5x - 2√3 and verify relationship
between the zeroes and its coefficients.​

Answer 1

$4 \sqrt{3} {x}^{2} + 5x - 2 \sqrt{3} \\ = 4 \sqrt{3} {x}^{2} + 8x - 3x - 2 \sqrt{3} \\ = 4x( \sqrt{3} x + 2) - \sqrt{3} ( \sqrt{3} x + 2) \\ = (4x - \sqrt{3} )( \sqrt{3} x + 2) \\ x = \frac{ \sqrt{3} }{4} \: or \: \: x = \frac{ - 2}{ \sqrt{3} } \\ \\ Verification : - \\ \alpha + \beta = \frac{ \sqrt{3} }{4} + \frac{ - 2}{ \sqrt{3} } = \frac{3 - 8 }{4 \sqrt{3} } = \frac{ - 5}{ 4\sqrt{3} } = \frac{ - b}{a} \\ \alpha \beta = \frac{ \sqrt{3} }{4} \times \frac{ - 2}{ \sqrt{3} } = \frac{ - 1}{2} = \frac{c}{a}$