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If the discriminant of b2-4ac in the quadratic equation formula is less than zero then the equation will have no real roots.

Q: What happens in the quadratic formula that yields no real solutions?

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Assuming the equation is 2b2+5b-35=0, the quadratic formula is one way to solve this equation. It can't be factored easily. Do not confuse the "b" variable in the formula given with the "b" in the related link. The values of a, b, & c are as follows to be used in the quadratic formula: a=2, b=5, c= -35. Placing these values in the quadratic formula gives: (-5+/- sqrt(52-4*2*(-35)))/(2*2). This yields variable b = (-5+/- sqrt(305))/4 or (-5+17.46425)/4 & (-5-17.46425)/4 = 3.11606 & -5.61606 which are the two roots of the given equation.

Per the formula in the related link, substitution into the formula yields (3*12)1/2, which is (36)1/2 or 6.

Where pi (~ 3.1416) is represented by π, The formula C= πr2 yields the formula r2 = (C/π) therefore r = square root (C/π). ...which is the same as : r = (C/π)1/2.

The formula is pi X radius2 X height. Application of this formula yields a value of about 1.130973355 X 103 of the cubic units corresponding to the length unit for the radius and height.

It's a fraction, like 5/10 or 1/2 or... divide the numerator by the denominator. Example: 5 divided by 10 or 1 divided by two. This yields the simple percentage.

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Assuming the equation is 2b2+5b-35=0, the quadratic formula is one way to solve this equation. It can't be factored easily. Do not confuse the "b" variable in the formula given with the "b" in the related link. The values of a, b, & c are as follows to be used in the quadratic formula: a=2, b=5, c= -35. Placing these values in the quadratic formula gives: (-5+/- sqrt(52-4*2*(-35)))/(2*2). This yields variable b = (-5+/- sqrt(305))/4 or (-5+17.46425)/4 & (-5-17.46425)/4 = 3.11606 & -5.61606 which are the two roots of the given equation.

Using your ICE table in doing equilibrium calculations of concentrations in chemistry yields a quadratic function. X = Vot +(1/2)at2 is an equation of kinematics in physics.

A base

6CO2+6H2O ----yields(sunlight)---- C6H12O6+6CO2

When b^2=4ac the zero is at a single point. The parabola does not penetrate the x axis. This represents two zeros, both with the same value. Example: x^2+4x+4 yields two zeros, each at x=-2. Notice that b^2=16=4ac. So Bob's your uncle!

pottasium bisulfate((HSO4)1-) K+ + (HSO4)1- yields KHSO4

When dissolved in water, an Arrhenius base yields hydroxide ions (OH⁻) as the only negative ions in solution. This is because Arrhenius bases are substances that increase the concentration of hydroxide ions in aqueous solutions.

The word equation for the formula 2Mg O2 yields 2MgO would be: "Two magnesium atoms react with one oxygen molecule to produce two magnesium oxide compounds."

Per the formula in the related link, substitution into the formula yields (3*12)1/2, which is (36)1/2 or 6.

2.81169x10^-12 J

The reaction between liquid bromine (Br2) and nitrogen gas (N2) yields nitrogen tribromide (NBr3) formula. The balanced chemical equation for the reaction is: 3 Br2 + N2 -> 2 NBr3

( In this explanation, SQRT(#) should be taken to mean the square root of a number, while (+/-) means plus or minus) In order to factor a quadratic expression such as this, it is necessary to use the quadratic formula. The formula is X= (-b (+/-) SQRT((b^2)-4ac))/2a, where the equation is in the for aX^2 + bX + C. So in our case, for 10X^2 - 9X -202: a= 10 b= -9 c= -202 Plugging these number into the quadratic formula yields X= (-(-9) (+/-) SQRT(((-9)^2)-4(10)(-202)))/2(10). After some calculator work, we get X= (9 (+/-) 90.33825)/ 20. Next, split the (+/-) into two equations: X= (9+90.33825)/20 and X= (9-90.33825)/20 Then, solve! X= (99.33825)/20 and X= (-81.33825)/20 X= (99.33825)/20 and X= (-81.33825)/20 X= 4.9669 and X= -4.0669