Solve the equation. 6x=2x^2+1

1 answer:

7 0

6x = 2x^2 + 1
2x^2 - 6x + 1 = 0
$x= \frac{-(-6) \pm \sqrt{(-6)^2-(4 \times 2 \times 1)}}{2 \times 2}\\=\frac{6\pm\sqrt{36-8}}{4}\\=\frac{6\pm\sqrt{28}}{4}\\=\frac{6\pm2\sqrt{7}}{4}\\=\frac{3\pm\sqrt{7}}{2}\\=\frac{3+\sqrt{7}}{2}\,or\,\frac{3-\sqrt{7}}{2}$

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Option D) $-2y(2y^4-3y^2-4y+1)$ is correct

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Step-by-step explanation:

Given polynomial is $-4y^5+6y^3+8y^2-2y$

To factorise the given polynomial by taking out the common terms of the given polynomial :

$-4y^5+6y^3+8y^2-2y$
$=2y(-2y^4+3y^2+4y-1)$ ( here 2y is GCF common term so taking outside the terms of the polynomial )
$=-2y(2y^4-3y^2-4y+1)$ ( now taking (-) outside )

Therefore $-4y^5+6y^3+8y^2-2y=-2y(2y^4-3y^2-4y+1)$

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