p(x)=-5x^2-10x-2-এর সমাধান করুন

$$p ( x ) = - 5 x ^ { 2 } - 10 x - 2$$

Factor

$$-5\left(x-\left(-\frac{\sqrt{15}}{5}-1\right)\right)\left(x-\left(\frac{\sqrt{15}}{5}-1\right)\right)$$

Steps Using the Quadratic Formula

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

$$-5x^{2}-10x-2=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$x=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\left(-5\right)\left(-2\right)}}{2\left(-5\right)}$$

Square -10.

$$x=\frac{-\left(-10\right)±\sqrt{100-4\left(-5\right)\left(-2\right)}}{2\left(-5\right)}$$

Multiply -4 times -5.

$$x=\frac{-\left(-10\right)±\sqrt{100+20\left(-2\right)}}{2\left(-5\right)}$$

Multiply 20 times -2.

$$x=\frac{-\left(-10\right)±\sqrt{100-40}}{2\left(-5\right)}$$

Add 100 to -40.

$$x=\frac{-\left(-10\right)±\sqrt{60}}{2\left(-5\right)}$$

Take the square root of 60.

$$x=\frac{-\left(-10\right)±2\sqrt{15}}{2\left(-5\right)}$$

The opposite of -10 is 10.

$$x=\frac{10±2\sqrt{15}}{2\left(-5\right)}$$

Multiply 2 times -5.

$$x=\frac{10±2\sqrt{15}}{-10}$$

Now solve the equation x=\frac{10±2\sqrt{15}}{-10} when ± is plus. Add 10 to 2\sqrt{15}.

$$x=\frac{2\sqrt{15}+10}{-10}$$

Divide 10+2\sqrt{15} by -10.

$$x=-\frac{\sqrt{15}}{5}-1$$

Now solve the equation x=\frac{10±2\sqrt{15}}{-10} when ± is minus. Subtract 2\sqrt{15} from 10.

$$x=\frac{10-2\sqrt{15}}{-10}$$

Divide 10-2\sqrt{15} by -10.

$$x=\frac{\sqrt{15}}{5}-1$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -1-\frac{\sqrt{15}}{5} for x_{1} and -1+\frac{\sqrt{15}}{5} for x_{2}.

$$-5x^{2}-10x-2=-5\left(x-\left(-\frac{\sqrt{15}}{5}-1\right)\right)\left(x-\left(\frac{\sqrt{15}}{5}-1\right)\right)$$

Evaluate

$$-5x^{2}-10x-2$$