Question

2x square +x+4 by completing the square method

Answer 1

$\large{\underline{\bf{\green{Given:-}}}}$

✰ p(x) = 2x² +x +4 = 0

$\large{\underline{\bf{\green{To\:Find:-}}}}$

✰ we need to find the roots of the given polynomial.

$\huge{\underline{\bf{\red{Solution:-}}}}$

$: \implies \sf\:2x^2+x+4=0$

$: \implies \sf\:2x^2+x=-4$

$\sf\: Divide\:both\:side\:by\:2$

$: \implies \sf\:\frac{2x^2+x}{2}=\frac{-4}{2}$

$: \implies \sf\:x^2+\frac{x}{2}=-2$

$\sf\:Add\:(\frac{1}{4})^2\:on\:both\:sides$

$: \implies \sf\:x^2+\frac{x}{2}+\frac{1}{16}=-2+\frac{1}{16}$

$: \implies \sf\:(x+\frac{1}{4})^2=\frac{-32+1}{16}$

$: \implies \sf\:(x+\frac{1}{4})^2=\frac{-31}{16}$

$: \implies \sf\:x+\frac{1}{4}= \sqrt{ \frac{ - 31}{16} }$

$: \implies \sf\:x+\frac{1}{4}= \frac{ \sqrt{31} }{4}$

$: \implies \bf{\purple{\:x = \frac{ \sqrt{31} - 1 }{4}}}$

$: \implies \bf{\purple{\:x = \frac{ - \sqrt{31} - 1}{4}}}$

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Answer 2

Answer:

$\implies$ x = (-√-31 - 1)/4

$\large\underline\mathrm{Given:-}$

• P(x) = 2x² + x + 4 = 0

$\large\underline\mathrm{To \: find}$

• We need to find the roots of the given polynomial.

$\large\underline\mathrm{Solution}$

$\implies$ 2x² + x + 4 = 0

$\implies$ 2x + x = -4

• Divide both side by 2.

$\implies$ (2x² + x)/2 = -4/2

$\implies$ x² + x/2 = -2

• Adding the (1/4)² on both sides.

$\implies$ x² + x/2 + 1/16 = -2 + 1/16

$\implies$ (x + 1/4)² = -31/16

$\implies$ x + x/4 = √-31/16

$\implies$ x + x/4 = √-31/4

$\implies$ x = (√-31 - 1)/4

$\implies$ x = (-√-31 - 1)/4