Factor
4\left(a-\frac{1-\sqrt{2}}{2}\right)\left(a-\frac{\sqrt{2}+1}{2}\right)
Evaluate
4a^{2}-4a-1
শেয়ার করুন
ক্লিপবোর্ডে কপি করা হয়েছে
4a^{2}-4a-1=0
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.
a=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\times 4\left(-1\right)}}{2\times 4}
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.
a=\frac{-\left(-4\right)±\sqrt{16-4\times 4\left(-1\right)}}{2\times 4}
Square -4.
a=\frac{-\left(-4\right)±\sqrt{16-16\left(-1\right)}}{2\times 4}
Multiply -4 times 4.
a=\frac{-\left(-4\right)±\sqrt{16+16}}{2\times 4}
Multiply -16 times -1.
a=\frac{-\left(-4\right)±\sqrt{32}}{2\times 4}
Add 16 to 16.
a=\frac{-\left(-4\right)±4\sqrt{2}}{2\times 4}
Take the square root of 32.
a=\frac{4±4\sqrt{2}}{2\times 4}
The opposite of -4 is 4.
a=\frac{4±4\sqrt{2}}{8}
Multiply 2 times 4.
a=\frac{4\sqrt{2}+4}{8}
Now solve the equation a=\frac{4±4\sqrt{2}}{8} when ± is plus. Add 4 to 4\sqrt{2}.
a=\frac{\sqrt{2}+1}{2}
Divide 4+4\sqrt{2} by 8.
a=\frac{4-4\sqrt{2}}{8}
Now solve the equation a=\frac{4±4\sqrt{2}}{8} when ± is minus. Subtract 4\sqrt{2} from 4.
a=\frac{1-\sqrt{2}}{2}
Divide 4-4\sqrt{2} by 8.
4a^{2}-4a-1=4\left(a-\frac{\sqrt{2}+1}{2}\right)\left(a-\frac{1-\sqrt{2}}{2}\right)
Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{1+\sqrt{2}}{2} for x_{1} and \frac{1-\sqrt{2}}{2} for x_{2}.
উদাহরণ
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