Question

if alpha and beta are the zeros of the quadratic polynomial 4x^2+4x+1​

Answer 1

$\huge\boxed{\underline{\bf { \red S \green O \pink L \blue U \orange T \purple I \red O \pink N \green{..}}}}$

$\longmapsto \sf {4x}^{2} + 4x + 1$

By splitting middle term

$\longmapsto \sf {4x}^{2} + 2x + 2x + 1$

$\longmapsto \sf2x(2x + 1) + 1(2x + 1)$

$\longmapsto \sf(2x + 1)(2x + 1)$

To find zeros of the quadratic polynomial

$\longmapsto \sf(2x + 1)(2x + 1) = 0$

$\longmapsto \sf(2x + 1) = 0$

$\longmapsto \sf2x = - 1$

$\longmapsto \sf x = - \frac{1}{2}$

Therefore

$\large:\implies \boxed{\sf \alpha = - \frac{1}{2}}$

$\large:\implies \boxed{\sf \beta = - \frac{1}{2}}$

Answer 2

Step-by-step explanation:

If

$\alpha \: and \: \beta \: are \: the \: zeroes \: of \: the \: poynomial \: \\ then \: \: the \:sum \: of \: zeroes \: \alpha + \beta = \frac{ - b}{a} \\ = \frac{ - 4}{4} = - 1 \\ product \: of \: zeroes \: \alpha \beta \: = \frac{c}{a} \\ = \frac{1}{4}$