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:

4x² + 4x + 1

By splitting middle term

4x² + 2x + 2x + 1

→→ 2x(2x + 1) + 1(2x + 1)

→→ (2x + 1) (2x + 1)

To find zeros of the quadratic polynomial

→ (2x + 1)(2x + 1) = 0

→ (2x + 1) = 0

2x = -1

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