Question

solve the quadratic equation by using formula 5m²+5m=1
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Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

The roots of 5m²+5m-1 are  $\alpha =\frac{-5+3\sqrt{5} }{10}$ and  $\beta =\frac{-5-3\sqrt{5} }{10}$

Explanation:

Given:

5m²+5m=1

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To find:

The roots

Formula:

$\alpha =\frac{-b+\sqrt{b^2-{4ac} } }{2a}$

$\beta =\frac{-b-\sqrt{b^2{-4ac} } }{2a}$

Solution:

==>  5m²+5m=1

==>  5m²+5m-1 =0

==> a = coefficient of m²

==> b = Coefficient of m

==> c = constant

==> a = 5

==> b = 5

==> c = -1

==> Substitute the values in the formula

==> $\alpha =\frac{-b+\sqrt{b^2-{4ac} } }{2a}$

==> $\alpha =\frac{-5+\sqrt{5^2{-4(5)(-1)} } }{2(5)}$

==> $\alpha =\frac{-5+\sqrt{25 {-4(-5)} } }{10}$

==> $\alpha =\frac{-5+\sqrt{25 {+20} } }{10}$

==> $\alpha =\frac{-5+\sqrt{45 } }{10}$

==> $\alpha =\frac{-5+\sqrt{5\times3\times3} }{10}$

==> $\alpha =\frac{-5+3\sqrt{5} }{10}$

==> $\beta =\frac{-b-\sqrt{b^2-{4ac} } }{2a}$

==> $\beta =\frac{-5-\sqrt{5^2{-4(5)(-1)} } }{2(5)}$

==> $\beta =\frac{-5-\sqrt{25 {-4(-5)} } }{10}$

==> $\beta =\frac{-5-\sqrt{25 {+20} } }{10}$

==> $\beta =\frac{-5-\sqrt{45 } }{10}$

==> $\beta =\frac{-5-\sqrt{5\times3\times3} }{10}$

==> $\beta =\frac{-5-3\sqrt{5} }{10}$

The roots of 5m²+5m-1 are  $\alpha =\frac{-5+3\sqrt{5} }{10}$ and  $\beta =\frac{-5-3\sqrt{5} }{10}$