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What is 2 to the power of 0 why?
20 = 1Consider what is the value of 2a ÷ 2a? Any number divided by itself is 1. Thus:2a ÷ 2a = 1The law of indices says that when dividing, they are subtracted, for example:25 ÷ 22 = (2 x 2 x 2 x 2 x 2) ÷ (2 x 2) = 2 x 2 x 2 = 23 = 25-2So 2a ÷ 2a is (also):2a ÷ 2a = 2a-a = 20Since any number subtracted from itself is 0 (= a - a). This must have the same value as before, thus:20 = 1The 2 above can be replaced by any number x which means that any number to the power 0 is 1:x0 = 1
What is x plus 2a?
x + 2a
Where did the quadratic equation come from?
The quadratic formula originated from the concept of completing the square. let's take ax2 + bx + c = 0. To complete the square, solve for x. Subtract c. ax2 + bx = -c. Then divide by a [notice- if there is no a value, then a=1]. x2 + bx/a = -c/a. Add (b/2a)2 to both sides. x2 + bx/a + b2/4a2 = -c/a + b2/4a2 Factor/Reformat. (x + b/2a)2 = (b2-4ac) / 4a2 (x + b/2a)2 = [(b2-4ac) / 2a]2 Square-root both sides. x + b/2a = ± √(b2-4ac) / 2a Subtract b/2a. x = -b/2a ± √(b2-4ac) / 2a Combine terms. x = [-b ± √(b2-4ac)] / 2a
What are the roots of x squared plus 8x plus 25?
We will use a tool called a quadratic formula. First, I will prove it. For all degree two function f(x) = ax^2 + bx + c where a, b, c are constants, claim the roots are -b +/- sqrt(b^2 - 4ac))/2a IF a is not 0 and b^2 - 4ac >= 0. Proof. Suppose the conditions are satisfied, finding the roots of the function is the same as solving the following ax^2 + bx + c = 0 we will simplify, since a != 0 a(x^2 + (b/a)x) + c = 0 we will do a trick, a trick that you see once, you will never forget, we add then subtract the same thing a(x^2 + (b/a)x + b^2/(4a^2) - b^2/(4a^2)) + c = 0 Now notice b/a = 2 . b/2a, we will do that, also, we will take -b^2/(4a^2) out, notice, b^2/4a^2 = (b/2a)^2 Then we get a (-b^2/(4a^2)) + a( x^2 + 2 (b/2a)x + (b/2a)^2) + c = 0 we use the complete square identity -b^2/(4a) + a(x + b/2a)^2 + c = 0 Isolate x a(x + b/2a)^2 = -c + b^2/4a = (-4ac + b^2)/4a (x + b/2a)^2 = (b^2 - 4ac)/(4a^2) (x + b/2a) = +/- sqrt (b^2 - 4ac) / 2a x = +/- sqrt (b^2 - 4ac) / 2a - b/2a x = -b +/- sqrt(b^2 - 4ac))/2a Q.E.D Now apply the quadratic formula to your question: x^2 + 8x + 25. First check if a = 0, a = 1 != 0, pass. Now check if b^2 - 4ac is non-negative. 8^2 - 4 x 1 x 25 = 64 - 100 = - 36 < 0. Done, this function have no roots.
What is a quadratic equation?
A quadratic equation is an equation where a quadratic polynomial is equal to zero. It can be written as ax^2+bx+c=0 where a,b,c are the coefficients and x is the variable. A quadratic equation has always two complex solutions for x given by the formula x=-b/2a+sqrt(b^2-4ac)/2a and x=-b/2a-sqrt(b^2-4ac)/2a. Examples of quadratic equations are x^2+x-2=0, 5x^2+6x=0, x^2+1=0 etc.
