How do you solve $- 5 x^{2} + 10 x + 15 = 0$ $-5x^2 + 10x + 15 = 0$ ?

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How do you solve $- 5 x^{2} + 10 x + 15 = 0$ $-5x^2 + 10x + 15 = 0$ ?

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Answer 1 · 2016-06-18T22:33:18

$x = - 1 or x = 3$ $x=-1 or x=3$

Explanation:

$- 5 x^{2} + 10 x + 15 = 0$ $-5x^2+10x+15=0$
$= - 5 (x^{2} - 2 x - 3) = 0$ $=-5(x^2-2x-3)=0$
To factorize the polynomial $x^{2} - 2 x - 3$ $x^2-2x-3$ in the form $(x + a) (x + b)$ $(x+a)(x+b)$
we have to find two integers $a$ $a$ and $b$ $b$ such that
$a + b = - 2$ $a+b=-2$ and $a \cdot b = - 3$ $a*b=-3$

check for $a = 1$ $a=1$ and $b = - 3$ $b=-3$
so, $(x^{2} - 2 x - 3) = (x + 1) (x - 3)$ $color(blue)((x^2-2x-3)=(x+1)(x-3))$

$- 5 x^{2} + 10 x + 15 = 0$ $-5x^2+10x+15=0$
$\Rightarrow - 5 (x + 1) (x - 3) = 0$ $rArr-5(x+1)(x-3)=0$

Knowing that if the product is zero then one of the factors can be equal to zero .

Since $- 5 \neq 0$ $-5!=0$
Therefore,

$x + 1 = 0$ $x+1=0$
$x = - 1$ $x=-1$

Or,
$x - 3 = 0$ $x-3=0$
$x = 3$ $x=3$

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How do you solve $- 5 x^{2} + 10 x + 15 = 0$ $-5x^2 + 10x + 15 = 0$ ?

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Explanation:

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