Question

Find the zeroes of the following
quaderatio polynomial and verify the
relationship blw the zeroes & the
coefficients .4x^2-3x-1​

Answer 1

$\huge\underline\mathfrak{SolUtiOnS}$

$\huge\implies \large\sf \:4 {x}^{2} - 3x - 1 \\ \\ \huge \implies \large \sf { x}^{2} - 4x + x - 1 \\ \\ \huge \implies \large \sf \: 4x(x - 1) + 1(x - 1) \\ \\ \huge \implies \large \sf (4x + 1)(x - 1)$

$\huge\bold\implies$$\huge\boxed{X =\frac{-1}{4}\; X=\:1 }$

$\huge\underline\mathrm\red{verifying\: the\: relationship}$

$\implies \large \tt \alpha + \beta = \frac{ - b}{a} \\ \implies \large \tt \frac{ - 1}{4} + 1 = \frac{3}{4}$

$\implies\large \tt \alpha \times \beta = \frac{c}{a} \\ \implies \: \large \tt \frac{ - 1}{4} \times 1 = \frac{ - 1}{4}$

$\huge{\underline{\tt{Hence\; verified}}}$