Question

factorisation 5x²-4x-7=0​

Answer 1

Step-by-step explanation:

$5x ^ { 2 } -4x-7$

Quadratic equations such as this one can be solved by a new direct factoring method that does not require guess work. To use the direct factoring method, the equation must be in the form x^2+Bx+C=0.This is achieved by dividing both sides of the equation by 5

2.

$x ^ 2 -\frac{4}{5}x -\frac{7}{5} = 0$

Let r and s be the factors for the quadratic equation such that x^2+Bx+C=(x−r)(x−s) where sum of factors (r+s)=−B and the product of factors rs = C

3.

$r + s = \frac{4}{5} rs = -\frac{7}{5}$

$(\frac{2}{5} - u) (\frac{2}{5} + u) = -\frac{7}{5}$

Simplify by expanding (a -b) (a + b) = a^2 – b^2

$\frac{4}{25} - u^2 = -\frac{7}{5}$

Simplify the expression by subtracting \frac{4}{25} on both sides

$-u^2 = -\frac{7}{5}-\frac{4}{25} = -\frac{39}{25}$

Simplify the expression by multiplying -1 on both sides and take the square root to obtain the value of unknown variable u

$u^2 = \frac{39}{25} u = \pm\sqrt{\frac{39}{25}} = \pm \frac{\sqrt{39}}{5}$

The factors r and s are the solutions to the quadratic equation. Substitute the value of u to compute the r and s.

$r =\frac{2}{5} - \frac{\sqrt{39}}{5} = -0.849 s = \frac{2}{5} + \frac{\sqrt{39}}{5} = 1.649$

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